# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.ba1 7056r2 $$[0, 0, 0, -1155, 13426]$$ $$665500/81$$ $$20739898368$$ $$$$ $$4096$$ $$0.71000$$
7056.ba2 7056r1 $$[0, 0, 0, 105, 1078]$$ $$2000/9$$ $$-576108288$$ $$$$ $$2048$$ $$0.36342$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7056.2.a.ba

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. 