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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 38640.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.c1 | 38640d4 | \([0, -1, 0, -97296256, 324018123616]\) | \(49737293673675178002921218/6641736806881023047235\) | \(13602276980492335200737280\) | \([2]\) | \(8847360\) | \(3.5503\) | |
| 38640.c2 | 38640d2 | \([0, -1, 0, -93934856, 350444105856]\) | \(89516703758060574923008036/1985322833430374025\) | \(2032970581432703001600\) | \([2, 2]\) | \(4423680\) | \(3.2038\) | |
| 38640.c3 | 38640d1 | \([0, -1, 0, -93934356, 350448022656]\) | \(358061097267989271289240144/176126855625\) | \(45088475040000\) | \([2]\) | \(2211840\) | \(2.8572\) | \(\Gamma_0(N)\)-optimal |
| 38640.c4 | 38640d3 | \([0, -1, 0, -90581456, 376619404896]\) | \(-40133926989810174413190818/6689384645060302103835\) | \(-13699859753083498708654080\) | \([2]\) | \(8847360\) | \(3.5503\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.c have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.c do not have complex multiplication.Modular form 38640.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
