Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 50193p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50193.r1 | 50193p1 | \([0, 0, 1, -13689, 637679]\) | \(-2985984/121\) | \(-11495735867187\) | \([]\) | \(147744\) | \(1.2739\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 50193p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 50193p do not have complex multiplication.Modular form 50193.2.a.p
sage: E.q_eigenform(10)