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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 42350ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42350.db1 | 42350ca1 | \([1, -1, 1, -543555, -166629053]\) | \(-1026590625/100352\) | \(-1736129780000000000\) | \([]\) | \(1570800\) | \(2.2408\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42350ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 42350ca do not have complex multiplication.Modular form 42350.2.a.ca
sage: E.q_eigenform(10)