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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 3234.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3234.a1 | 3234e1 | \([1, 1, 0, -4869, -137619]\) | \(-260607143968297/11270993184\) | \(-552278666016\) | \([]\) | \(8400\) | \(1.0188\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 3234.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 3234.a do not have complex multiplication.Modular form 3234.2.a.a
sage: E.q_eigenform(10)