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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 312312.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
312312.bz1 | 312312bz1 | \([0, 1, 0, -280596, 59160453]\) | \(-31636584484096/1331669031\) | \(-102843393021633264\) | \([]\) | \(3231360\) | \(2.0309\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 312312.bz1 has rank \(1\).
Complex multiplication
The elliptic curves in class 312312.bz do not have complex multiplication.Modular form 312312.2.a.bz
sage: E.q_eigenform(10)