# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.m1 7056bw2 $$[0, 0, 0, -131376, 18343024]$$ $$-1713910976512/1594323$$ $$-233270525472768$$ $$[]$$ $$24960$$ $$1.6798$$
7056.m2 7056bw1 $$[0, 0, 0, -336, -2576]$$ $$-28672/3$$ $$-438939648$$ $$[]$$ $$1920$$ $$0.39737$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 7056.m do not have complex multiplication.

## Modular form7056.2.a.m

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.