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SageMath
E = EllipticCurve("hf1")
E.isogeny_class()
Elliptic curves in class 193200.hf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193200.hf1 | 193200bp1 | \([0, 1, 0, 7387, 83058]\) | \(111431820247040/71501334387\) | \(-28600533754800\) | \([]\) | \(608832\) | \(1.2710\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 193200.hf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 193200.hf do not have complex multiplication.Modular form 193200.2.a.hf
sage: E.q_eigenform(10)