Show commands:
SageMath
E = EllipticCurve("hr1")
E.isogeny_class()
Elliptic curves in class 338800hr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338800.hr1 | 338800hr1 | \([0, -1, 0, -3428, -181993]\) | \(-6288640/16807\) | \(-11909850290800\) | \([]\) | \(686400\) | \(1.1965\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 338800hr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 338800hr do not have complex multiplication.Modular form 338800.2.a.hr
sage: E.q_eigenform(10)