# Properties

 Label 7056bp Number of curves 6 Conductor 7056 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 7056bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.bd5 7056bp1 [0, 0, 0, -3675, -173558] [2] 9216 $$\Gamma_0(N)$$-optimal
7056.bd4 7056bp2 [0, 0, 0, -74235, -7779926] [2] 18432
7056.bd6 7056bp3 [0, 0, 0, 31605, 3629626] [2] 27648
7056.bd3 7056bp4 [0, 0, 0, -250635, 39587002] [2] 55296
7056.bd2 7056bp5 [0, 0, 0, -1203195, 509453098] [2] 82944
7056.bd1 7056bp6 [0, 0, 0, -19266555, 32550241066] [2] 165888

## Rank

sage: E.rank()

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

## Modular form7056.2.a.bd

sage: E.q_eigenform(10)

$$q + 4q^{13} + 6q^{17} + 2q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.