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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 68400bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68400.fn1 | 68400bm1 | \([0, 0, 0, -1875, -44750]\) | \(-31250/19\) | \(-443232000000\) | \([]\) | \(69120\) | \(0.93685\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 68400bm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 68400bm do not have complex multiplication.Modular form 68400.2.a.bm
sage: E.q_eigenform(10)