# Properties

 Label 7056.ca Number of curves $2$ Conductor $7056$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.ca1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.ca1 7056cc2 [0, 0, 0, -19803, 1043210]  24576
7056.ca2 7056cc1 [0, 0, 0, 357, 55370]  12288 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7056.ca have rank $$0$$.

## Modular form7056.2.a.ca

sage: E.q_eigenform(10)

$$q + 4q^{5} - 4q^{11} - 4q^{13} + 4q^{19} + O(q^{20})$$

## 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. 