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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 127050.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127050.r1 | 127050g1 | \([1, 1, 0, -28800, 2592000]\) | \(-1397395501513/740710656\) | \(-1400406084000000\) | \([]\) | \(829440\) | \(1.6104\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 127050.r1 has rank \(2\).
Complex multiplication
The elliptic curves in class 127050.r do not have complex multiplication.Modular form 127050.2.a.r
sage: E.q_eigenform(10)