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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 418600.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 418600.c1 | 418600c1 | \([0, 1, 0, -5887400233, -173875470618837]\) | \(5642017163771722268092767232/570626054098424597\) | \(2282504216393698388000000\) | \([]\) | \(304128000\) | \(4.1048\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 418600.c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 418600.c do not have complex multiplication.Modular form 418600.2.a.c
sage: E.q_eigenform(10)