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SageMath
E = EllipticCurve("hd1")
E.isogeny_class()
Elliptic curves in class 193200hd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193200.b1 | 193200hd1 | \([0, -1, 0, 352, 2832]\) | \(187878620/255507\) | \(-6540979200\) | \([]\) | \(117504\) | \(0.56918\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 193200hd1 has rank \(2\).
Complex multiplication
The elliptic curves in class 193200hd do not have complex multiplication.Modular form 193200.2.a.hd
sage: E.q_eigenform(10)