# Properties

 Label 960.l Number of curves 8 Conductor 960 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("960.l1")

sage: E.isogeny_class()

## Elliptic curves in class 960.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
960.l1 960g7 [0, 1, 0, -138241, -19829665] [2] 2048
960.l2 960g5 [0, 1, 0, -8641, -311905] [2, 2] 1024
960.l3 960g8 [0, 1, 0, -7041, -429345] [2] 2048
960.l4 960g4 [0, 1, 0, -5121, 139359] [2] 512
960.l5 960g3 [0, 1, 0, -641, -3105] [2, 2] 512
960.l6 960g2 [0, 1, 0, -321, 2079] [2, 2] 256
960.l7 960g1 [0, 1, 0, -1, 95] [2] 128 $$\Gamma_0(N)$$-optimal
960.l8 960g6 [0, 1, 0, 2239, -20961] [2] 1024

## Rank

sage: E.rank()

The elliptic curves in class 960.l have rank $$0$$.

## Modular form960.2.a.l

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + 4q^{11} + 2q^{13} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.