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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 135240.cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135240.cr1 | 135240cz1 | \([0, 1, 0, -347916, 73368945]\) | \(50494475148544/3929765625\) | \(362469068876250000\) | \([]\) | \(1448832\) | \(2.1135\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 135240.cr1 has rank \(0\).
Complex multiplication
The elliptic curves in class 135240.cr do not have complex multiplication.Modular form 135240.2.a.cr
sage: E.q_eigenform(10)