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SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 92736ef
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.cq2 | 92736ef1 | \([0, 0, 0, 150900, 3330448]\) | \(7953970437500/4703287687\) | \(-224703068492464128\) | \([2]\) | \(737280\) | \(2.0188\) | \(\Gamma_0(N)\)-optimal |
| 92736.cq1 | 92736ef2 | \([0, 0, 0, -610860, 26792656]\) | \(263822189935250/149429406721\) | \(14278202163148750848\) | \([2]\) | \(1474560\) | \(2.3654\) |
Rank
sage: E.rank()
The elliptic curves in class 92736ef have rank \(0\).
Complex multiplication
The elliptic curves in class 92736ef do not have complex multiplication.Modular form 92736.2.a.ef
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.
