# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("j1")

E.isogeny_class()

## Elliptic curves in class 9025.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9025.j1 9025i2 $$[0, 0, 1, -2353625, -1389805469]$$ $$2045023375454208$$ $$705078125$$ $$[]$$ $$93600$$ $$1.9354$$
9025.j2 9025i1 $$[0, 0, 1, -2375, 44531]$$ $$2101248$$ $$705078125$$ $$[]$$ $$7200$$ $$0.65296$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form9025.2.a.j

sage: E.q_eigenform(10)

$$q + 2 q^{2} + 2 q^{4} + 4 q^{7} - 3 q^{9} - q^{11} - 2 q^{13} + 8 q^{14} - 4 q^{16} + 2 q^{17} - 6 q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.