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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 38640.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.cc1 | 38640ck1 | \([0, 1, 0, -1578421, -942814621]\) | \(-106177523183250079744/32201176731237675\) | \(-131896019891149516800\) | \([]\) | \(1008000\) | \(2.5746\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 38640.cc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 38640.cc do not have complex multiplication.Modular form 38640.2.a.cc
sage: E.q_eigenform(10)