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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4200c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4200.l1 | 4200c1 | \([0, -1, 0, 197672, 58827532]\) | \(16683494528422270/38919722282469\) | \(-1992689780862412800\) | \([]\) | \(66528\) | \(2.1954\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4200c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4200c do not have complex multiplication.Modular form 4200.2.a.c
sage: E.q_eigenform(10)