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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 194271.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
194271.j1 | 194271f1 | \([1, 0, 0, -1998654, -1088961153]\) | \(-1484391946907017/1946200179\) | \(-1157645253803574459\) | \([]\) | \(5040000\) | \(2.3729\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 194271.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 194271.j do not have complex multiplication.Modular form 194271.2.a.j
sage: E.q_eigenform(10)