# Properties

 Label 9025.h Number of curves $2$ Conductor $9025$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 9025.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9025.h1 9025g2 $$[1, -1, 0, -8912, -313929]$$ $$13312053/361$$ $$2122945380125$$ $$$$ $$11520$$ $$1.1456$$
9025.h2 9025g1 $$[1, -1, 0, 113, -16104]$$ $$27/19$$ $$-111733967375$$ $$$$ $$5760$$ $$0.79899$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form9025.2.a.h

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. 