# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.e1 7056be1 $$[0, 0, 0, -73059, -7601566]$$ $$-67645179/8$$ $$-5100326977536$$ $$[]$$ $$24192$$ $$1.4639$$ $$\Gamma_0(N)$$-optimal
7056.e2 7056be2 $$[0, 0, 0, 9261, -23467374]$$ $$189/512$$ $$-237960855463919616$$ $$[]$$ $$72576$$ $$2.0132$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7056.2.a.e

sage: E.q_eigenform(10)

$$q - 3q^{5} - 3q^{11} + 2q^{13} - 6q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 