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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 912.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 912.d1 | 912f2 | \([0, -1, 0, -70245, 7189389]\) | \(-9358714467168256/22284891\) | \(-91278913536\) | \([]\) | \(2400\) | \(1.3446\) | |
| 912.d2 | 912f1 | \([0, -1, 0, 315, 2349]\) | \(841232384/1121931\) | \(-4595429376\) | \([]\) | \(480\) | \(0.53984\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 912.d have rank \(1\).
Complex multiplication
The elliptic curves in class 912.d do not have complex multiplication.Modular form 912.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
