# Properties

 Label 7056.y Number of curves $2$ Conductor $7056$ CM -3 Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.y1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.y1 7056bc1 [0, 0, 0, 0, -784] [] 1728 $$\Gamma_0(N)$$-optimal
7056.y2 7056bc2 [0, 0, 0, 0, 21168] [] 5184

## Rank

sage: E.rank()

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

## Modular form7056.2.a.y

sage: E.q_eigenform(10)

$$q - 7q^{13} + 7q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 