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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 102550.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102550.c1 | 102550l1 | \([1, -1, 0, -4503367, 3628205041]\) | \(5171371652962916757/82860802004204\) | \(161837503914460937500\) | \([]\) | \(7284480\) | \(2.6777\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 102550.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 102550.c do not have complex multiplication.Modular form 102550.2.a.c
sage: E.q_eigenform(10)