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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 4002.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4002.r1 | 4002p1 | \([1, 0, 0, -1811224, 938072696]\) | \(-657113243203147908283777/368184\) | \(-368184\) | \([]\) | \(33120\) | \(1.7821\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4002.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4002.r do not have complex multiplication.Modular form 4002.2.a.r
sage: E.q_eigenform(10)