# Properties

 Label 7056.bo Number of curves $4$ Conductor $7056$ CM no Rank $1$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("bo1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bo1 7056x3 $$[0, 0, 0, -131859, -18429390]$$ $$1443468546/7$$ $$1229543110656$$ $$$$ $$24576$$ $$1.5202$$
7056.bo2 7056x4 $$[0, 0, 0, -26019, 1278018]$$ $$11090466/2401$$ $$421733286955008$$ $$$$ $$24576$$ $$1.5202$$
7056.bo3 7056x2 $$[0, 0, 0, -8379, -277830]$$ $$740772/49$$ $$4303400887296$$ $$[2, 2]$$ $$12288$$ $$1.1737$$
7056.bo4 7056x1 $$[0, 0, 0, 441, -18522]$$ $$432/7$$ $$-153692888832$$ $$$$ $$6144$$ $$0.82708$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7056.2.a.bo

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 