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SageMath
E = EllipticCurve("jm1")
E.isogeny_class()
Elliptic curves in class 78400jm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 78400.hz2 | 78400jm1 | \([0, 1, 0, -25153, 1663423]\) | \(-9317\) | \(-188900999168000\) | \([]\) | \(172032\) | \(1.4777\) | \(\Gamma_0(N)\)-optimal |
| 78400.hz1 | 78400jm2 | \([0, 1, 0, -652548353, -6416258962177]\) | \(-162677523113838677\) | \(-188900999168000\) | \([]\) | \(6365184\) | \(3.2832\) |
Rank
sage: E.rank()
The elliptic curves in class 78400jm have rank \(1\).
Complex multiplication
The elliptic curves in class 78400jm do not have complex multiplication.Modular form 78400.2.a.jm
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
