# Properties

 Label 7056.bb Number of curves $4$ Conductor $7056$ CM -3 Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.bb1 7056bf4 [0, 0, 0, -6615, -203742] [2] 6912
7056.bb2 7056bf2 [0, 0, 0, -735, 7546] [2] 2304
7056.bb3 7056bf3 [0, 0, 0, 0, -9261] [2] 3456
7056.bb4 7056bf1 [0, 0, 0, 0, 343] [2] 1152 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form7056.2.a.bb

sage: E.q_eigenform(10)

$$q - 2q^{13} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.