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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1077.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1077.a1 | 1077a1 | \([1, 1, 1, -27, 42]\) | \(2181825073/29079\) | \(29079\) | \([]\) | \(144\) | \(-0.33645\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1077.a1 has rank \(2\).
Complex multiplication
The elliptic curves in class 1077.a do not have complex multiplication.Modular form 1077.2.a.a
sage: E.q_eigenform(10)