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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 82800bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82800.ew1 | 82800bm1 | \([0, 0, 0, -45300, 3719500]\) | \(-3525581824/9315\) | \(-27162540000000\) | \([]\) | \(294912\) | \(1.4528\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82800bm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 82800bm do not have complex multiplication.Modular form 82800.2.a.bm
sage: E.q_eigenform(10)