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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 605.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
605.c1 | 605a1 | \([1, -1, 0, -1414, -44027]\) | \(-1459161/3125\) | \(-669871503125\) | \([]\) | \(1320\) | \(0.95811\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 605.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 605.c do not have complex multiplication.Modular form 605.2.a.c
sage: E.q_eigenform(10)