# Properties

 Label 56925q Number of curves 2 Conductor 56925 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("56925.m1")

sage: E.isogeny_class()

## Elliptic curves in class 56925q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
56925.m2 56925q1 [1, -1, 1, -5180, 2087822]  184320 $$\Gamma_0(N)$$-optimal
56925.m1 56925q2 [1, -1, 1, -278555, 56216072]  368640

## Rank

sage: E.rank()

The elliptic curves in class 56925q have rank $$1$$.

## Modular form 56925.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 2q^{7} + 3q^{8} - q^{11} - 2q^{13} - 2q^{14} - q^{16} + 2q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 