# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("7056.w1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.w1 7056bk2 [0, 0, 0, -995043, -396371486] [] 112896
7056.w2 7056bk1 [0, 0, 0, -7203, 542626] [] 16128 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form7056.2.a.w

sage: E.q_eigenform(10)

$$q - q^{5} + 5q^{11} + 4q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 