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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 40733.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40733.a1 | 40733e1 | \([1, 0, 0, -21699591, 38984528554]\) | \(-14429645772301489/34179505129\) | \(-2676630723068983006249\) | \([]\) | \(2627520\) | \(2.9915\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40733.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 40733.a do not have complex multiplication.Modular form 40733.2.a.a
sage: E.q_eigenform(10)