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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 14784a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14784.r1 | 14784a1 | \([0, -1, 0, -6825, -214767]\) | \(-34339609640704/916839\) | \(-938843136\) | \([]\) | \(11520\) | \(0.82662\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 14784a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 14784a do not have complex multiplication.Modular form 14784.2.a.a
sage: E.q_eigenform(10)