Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 28322c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28322.b1 | 28322c1 | \([1, -1, 0, -441646, 407309524]\) | \(-164384733177/1140850688\) | \(-66117206642914230272\) | \([]\) | \(1797120\) | \(2.4864\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 28322c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 28322c do not have complex multiplication.Modular form 28322.2.a.c
sage: E.q_eigenform(10)