# Properties

 Label 122694bd Number of curves 4 Conductor 122694 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("122694.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 122694bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
122694.bj3 122694bd1 [1, 0, 1, -112896, -13780934] [2] 1036800 $$\Gamma_0(N)$$-optimal
122694.bj4 122694bd2 [1, 0, 1, 91594, -58114366] [2] 2073600
122694.bj1 122694bd3 [1, 0, 1, -1646571, 809986582] [2] 3110400
122694.bj2 122694bd4 [1, 0, 1, -828611, 1615186406] [2] 6220800

## Rank

sage: E.rank()

The elliptic curves in class 122694bd have rank $$1$$.

## Modular form 122694.2.a.bj

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{12} - 2q^{14} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.