I am the oldest of a property left in succession. What are my rights cusdial rights in this succession?

If there was no will, the property gets passed by Intestate Succession, which means it goes according to the laws of your state:

First, it goes to the surviving spouse. 

A surviving spouse (not judicially separated from the decedent) is generally considered first when distributing assets, including the decedent's share of community (marital) and separate (nonmarital) property, from the intestate estate. However, the amount a surviving spouse is entitled to varies as follows:

• If the decedent leaves no descendants, the surviving spouse is entitled to all of the decedent's share of community property.
• If the decedent is survived by descendants, the surviving spouse gets the legal right to use (known as a "usufruct") decedent's share of community property for the rest of the surviving spouse's life or until remarriage (whichever occurs first).
• As for separate property, the surviving spouse has to wait in line after decedent's descendants, parents, and siblings or their descendants.

If there is no surviving spouse, it goes to heirs other than surviving spouse. Any part of the intestate estate not passing to the surviving spouse as indicated above, or the entire intestate estate if there is no surviving spouse, passes as follows in this order to the deceased's:

1. Descendants (children)
2. Parents.
3. Siblings.
4. Siblings' descendants.
5. Ascendants, starting with decedent's grandparents, in the nearest degree of kinship to the decedent.
6. Collateral relatives, in the nearest degree of kinship to the decedent.

If none of the above relatives exist, it goes to the State of Louisiana.

If there is not surviving spouse, you and your siblings get the property equally.  You will have to work together to make decisions on it.