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SageMath
E = EllipticCurve("hg1")
E.isogeny_class()
Elliptic curves in class 193200hg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193200.l1 | 193200hg1 | \([0, -1, 0, -235208, 48318912]\) | \(-143906968900/17253243\) | \(-172532430000000000\) | \([]\) | \(2177280\) | \(2.0428\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 193200hg1 has rank \(0\).
Complex multiplication
The elliptic curves in class 193200hg do not have complex multiplication.Modular form 193200.2.a.hg
sage: E.q_eigenform(10)