# Properties

 Label 7056.bc Number of curves $2$ Conductor $7056$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bc1 7056q2 $$[0, 0, 0, -56595, -4605118]$$ $$665500/81$$ $$2440028303096832$$ $$[2]$$ $$28672$$ $$1.6830$$
7056.bc2 7056q1 $$[0, 0, 0, 5145, -369754]$$ $$2000/9$$ $$-67778563974912$$ $$[2]$$ $$14336$$ $$1.3364$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7056.2.a.bc

sage: E.q_eigenform(10)

$$q + 4q^{13} - 4q^{17} + 4q^{19} + O(q^{20})$$

## 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.