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SageMath
E = EllipticCurve("hb1")
E.isogeny_class()
Elliptic curves in class 177600hb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177600.d1 | 177600hb1 | \([0, -1, 0, -53, -723]\) | \(-8192/111\) | \(-227328000\) | \([]\) | \(70656\) | \(0.28509\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 177600hb1 has rank \(1\).
Complex multiplication
The elliptic curves in class 177600hb do not have complex multiplication.Modular form 177600.2.a.hb
sage: E.q_eigenform(10)