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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 42153.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42153.a1 | 42153a1 | \([0, -1, 1, -6, 20]\) | \(-28094464/126459\) | \(-126459\) | \([]\) | \(9568\) | \(-0.33620\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42153.a1 has rank \(3\).
Complex multiplication
The elliptic curves in class 42153.a do not have complex multiplication.Modular form 42153.2.a.a
sage: E.q_eigenform(10)