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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4536.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4536.a1 | 4536a1 | \([0, 0, 0, -27, 135]\) | \(-2304/7\) | \(-6613488\) | \([]\) | \(1440\) | \(-0.0045464\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4536.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4536.a do not have complex multiplication.Modular form 4536.2.a.a
sage: E.q_eigenform(10)