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SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 193200.fm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193200.fm1 | 193200cq1 | \([0, 1, 0, -38533, 3384563]\) | \(-98867482624/20696067\) | \(-1324548288000000\) | \([]\) | \(960000\) | \(1.6234\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 193200.fm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 193200.fm do not have complex multiplication.Modular form 193200.2.a.fm
sage: E.q_eigenform(10)