Show commands:
SageMath
E = EllipticCurve("pl1")
E.isogeny_class()
Elliptic curves in class 235200pl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.pl1 | 235200pl1 | \([0, 1, 0, -39993, 3065103]\) | \(-805661175040/729\) | \(-6401203200\) | \([]\) | \(442368\) | \(1.1799\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 235200pl1 has rank \(1\).
Complex multiplication
The elliptic curves in class 235200pl do not have complex multiplication.Modular form 235200.2.a.pl
sage: E.q_eigenform(10)