# Properties

 Label 7056.f Number of curves $2$ Conductor $7056$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.f1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.f1 7056bo2 [0, 0, 0, -62769, -6052921] [] 15120
7056.f2 7056bo1 [0, 0, 0, -1029, -2401] [] 5040 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7056.f have rank $$1$$.

## Modular form7056.2.a.f

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 