# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.l1 7056i2 $$[0, 0, 0, -48951, -4167450]$$ $$21882096/7$$ $$4149707998464$$ $$$$ $$18432$$ $$1.3960$$
7056.l2 7056i1 $$[0, 0, 0, -2646, -83349]$$ $$-55296/49$$ $$-1815497249328$$ $$$$ $$9216$$ $$1.0494$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7056.2.a.l

sage: E.q_eigenform(10)

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