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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 52800.ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52800.ev1 | 52800cj2 | \([0, 1, 0, -733633, -267448417]\) | \(-6663170841705625/850403524608\) | \(-5573204538870988800\) | \([]\) | \(912384\) | \(2.3308\) | |
| 52800.ev2 | 52800cj1 | \([0, 1, 0, 58367, 849503]\) | \(3355354844375/1987172352\) | \(-13023132726067200\) | \([]\) | \(304128\) | \(1.7815\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 52800.ev have rank \(0\).
Complex multiplication
The elliptic curves in class 52800.ev do not have complex multiplication.Modular form 52800.2.a.ev
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
