Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 75150.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75150.r1 | 75150m1 | \([1, -1, 0, -734292, -242351384]\) | \(-3843995587427449/6390046584\) | \(-72786624370875000\) | \([]\) | \(1128960\) | \(2.1314\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75150.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75150.r do not have complex multiplication.Modular form 75150.2.a.r
sage: E.q_eigenform(10)