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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 20181a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20181.j1 | 20181a1 | \([0, -1, 1, 19861, 33915674]\) | \(1015808/583443\) | \(-497613305557689363\) | \([]\) | \(223200\) | \(2.0748\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 20181a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 20181a do not have complex multiplication.Modular form 20181.2.a.a
sage: E.q_eigenform(10)