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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 122694o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122694.s1 | 122694o1 | \([1, 1, 0, -16942, -1081868]\) | \(-14846689/5184\) | \(-187798958208576\) | \([]\) | \(418176\) | \(1.4501\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 122694o1 has rank \(2\).
Complex multiplication
The elliptic curves in class 122694o do not have complex multiplication.Modular form 122694.2.a.o
sage: E.q_eigenform(10)