# Properties

 Label 2496.p Number of curves $2$ Conductor $2496$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("p1")

E.isogeny_class()

## Elliptic curves in class 2496.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.p1 2496p1 $$[0, 1, 0, -2605, 47219]$$ $$1909913257984/129730653$$ $$132844188672$$ $$$$ $$3840$$ $$0.88296$$ $$\Gamma_0(N)$$-optimal
2496.p2 2496p2 $$[0, 1, 0, 2255, 207599]$$ $$77366117936/1172914587$$ $$-19217032593408$$ $$$$ $$7680$$ $$1.2295$$

## Rank

sage: E.rank()

The elliptic curves in class 2496.p have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2496.p do not have complex multiplication.

## Modular form2496.2.a.p

sage: E.q_eigenform(10)

$$q + q^{3} - 4 q^{5} + q^{9} + 2 q^{11} + q^{13} - 4 q^{15} + 2 q^{17} - 8 q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 