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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 126350x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126350.p1 | 126350x1 | \([1, 1, 0, 22711225, -83591796875]\) | \(1762396940073671/5127312834560\) | \(-3769046085382538240000000\) | \([]\) | \(23224320\) | \(3.3992\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 126350x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 126350x do not have complex multiplication.Modular form 126350.2.a.x
sage: E.q_eigenform(10)