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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 28042.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28042.a1 | 28042b1 | \([1, -1, 0, -19, 49]\) | \(-781229961/392588\) | \(-392588\) | \([]\) | \(16416\) | \(-0.22167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 28042.a1 has rank \(3\).
Complex multiplication
The elliptic curves in class 28042.a do not have complex multiplication.Modular form 28042.2.a.a
sage: E.q_eigenform(10)