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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 91728d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91728.g1 | 91728d1 | \([0, 0, 0, -38367, 2870910]\) | \(10536048/91\) | \(53946203980032\) | \([2]\) | \(516096\) | \(1.4593\) | \(\Gamma_0(N)\)-optimal |
| 91728.g2 | 91728d2 | \([0, 0, 0, -11907, 6760530]\) | \(-78732/8281\) | \(-19636418248731648\) | \([2]\) | \(1032192\) | \(1.8059\) |
Rank
sage: E.rank()
The elliptic curves in class 91728d have rank \(2\).
Complex multiplication
The elliptic curves in class 91728d do not have complex multiplication.Modular form 91728.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
