# Properties

 Label 7650by Number of curves 4 Conductor 7650 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7650.ci1")

sage: E.isogeny_class()

## Elliptic curves in class 7650by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7650.ci4 7650by1 [1, -1, 1, -680, -4053] [2] 6912 $$\Gamma_0(N)$$-optimal
7650.ci3 7650by2 [1, -1, 1, -9680, -364053] [2] 13824
7650.ci2 7650by3 [1, -1, 1, -23180, 1363947] [2] 20736
7650.ci1 7650by4 [1, -1, 1, -25430, 1084947] [2] 41472

## Rank

sage: E.rank()

The elliptic curves in class 7650by have rank $$1$$.

## Modular form7650.2.a.ci

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 4q^{7} + q^{8} - 6q^{11} - 2q^{13} + 4q^{14} + q^{16} - q^{17} - 4q^{19} + O(q^{20})$$

## 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 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.