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SageMath
E = EllipticCurve("io1")
E.isogeny_class()
Elliptic curves in class 127050.io
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127050.io1 | 127050hx1 | \([1, 0, 0, -1080813, 434929617]\) | \(-73853319448242961/501854330880\) | \(-948818344320000000\) | \([]\) | \(2695680\) | \(2.2841\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 127050.io1 has rank \(1\).
Complex multiplication
The elliptic curves in class 127050.io do not have complex multiplication.Modular form 127050.2.a.io
sage: E.q_eigenform(10)