# Properties

 Label 9025.c Number of curves $2$ Conductor $9025$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

## Elliptic curves in class 9025.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9025.c1 9025h2 $$[1, -1, 1, -222805, -39463928]$$ $$13312053/361$$ $$33171021564453125$$ $$[2]$$ $$57600$$ $$1.9503$$
9025.c2 9025h1 $$[1, -1, 1, 2820, -2010178]$$ $$27/19$$ $$-1745843240234375$$ $$[2]$$ $$28800$$ $$1.6037$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9025.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9025.c do not have complex multiplication.

## Modular form9025.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - 2 q^{7} + 3 q^{8} - 3 q^{9} - 4 q^{11} - 2 q^{13} + 2 q^{14} - q^{16} - 4 q^{17} + 3 q^{18} + O(q^{20})$$

## 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.