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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 88200io
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88200.be1 | 88200io1 | \([0, 0, 0, -180075, -15966650]\) | \(2450\) | \(263583304346880000\) | \([]\) | \(822528\) | \(2.0404\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 88200io1 has rank \(1\).
Complex multiplication
The elliptic curves in class 88200io do not have complex multiplication.Modular form 88200.2.a.io
sage: E.q_eigenform(10)