# Properties

 Label 7056.n Number of curves $2$ Conductor $7056$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.n1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.n1 7056bv2 [0, 0, 0, -19551, -974806] [2] 21504
7056.n2 7056bv1 [0, 0, 0, -4116, 84035] [2] 10752 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form7056.2.a.n

sage: E.q_eigenform(10)

$$q - 2q^{5} + 2q^{11} - 4q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.