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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 45693.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45693.a1 | 45693a1 | \([0, 0, 1, -63, -169]\) | \(37933056/5077\) | \(3701133\) | \([]\) | \(27776\) | \(-0.012084\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 45693.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 45693.a do not have complex multiplication.Modular form 45693.2.a.a
sage: E.q_eigenform(10)