# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bl1 7056bs2 $$[0, 0, 0, -20307, 1155602]$$ $$-6329617441/279936$$ $$-40958336434176$$ $$[]$$ $$16128$$ $$1.3769$$
7056.bl2 7056bs1 $$[0, 0, 0, -147, -1582]$$ $$-2401/6$$ $$-877879296$$ $$[]$$ $$2304$$ $$0.40398$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7056.2.a.bl

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 