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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 5850x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5850.l1 | 5850x1 | \([1, -1, 0, -2022867, 1176735541]\) | \(-3214683778008145/238496514048\) | \(-67915608883200000000\) | \([]\) | \(154560\) | \(2.5542\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5850x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 5850x do not have complex multiplication.Modular form 5850.2.a.x
sage: E.q_eigenform(10)