# Properties

 Label 7650.ca Number of curves 6 Conductor 7650 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7650.ca1")

sage: E.isogeny_class()

## Elliptic curves in class 7650.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7650.ca1 7650bz5 [1, -1, 1, -6242405, 6004666347] [2] 131072
7650.ca2 7650bz3 [1, -1, 1, -390155, 93893847] [2, 2] 65536
7650.ca3 7650bz6 [1, -1, 1, -369905, 104059347] [2] 131072
7650.ca4 7650bz2 [1, -1, 1, -25655, 1310847] [2, 2] 32768
7650.ca5 7650bz1 [1, -1, 1, -7655, -237153] [2] 16384 $$\Gamma_0(N)$$-optimal
7650.ca6 7650bz4 [1, -1, 1, 50845, 7583847] [2] 65536

## Rank

sage: E.rank()

The elliptic curves in class 7650.ca have rank $$0$$.

## Modular form7650.2.a.ca

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} + 4q^{11} + 2q^{13} + q^{16} + q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.