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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 271440.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271440.r1 | 271440r1 | \([0, 0, 0, 6912, 2920752]\) | \(452984832/45973265\) | \(-3706436710379520\) | \([]\) | \(1271808\) | \(1.6668\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 271440.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 271440.r do not have complex multiplication.Modular form 271440.2.a.r
sage: E.q_eigenform(10)