# Properties

 Label 7056.c Number of curves 2 Conductor 7056 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.c1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.c1 7056ba2 [0, 0, 0, -17787, 902090]  18432
7056.c2 7056ba1 [0, 0, 0, -147, 37730]  9216 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7056.c have rank $$1$$.

## Modular form7056.2.a.c

sage: E.q_eigenform(10)

$$q - 4q^{5} - 2q^{17} - 2q^{19} + O(q^{20})$$

## 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 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. 