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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 126350.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126350.a1 | 126350j1 | \([1, -1, 0, -40157569492, -3097403860376084]\) | \(2272707362766267675/67228\) | \(211852036584830195312500\) | \([]\) | \(314640000\) | \(4.4334\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 126350.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 126350.a do not have complex multiplication.Modular form 126350.2.a.a
sage: E.q_eigenform(10)