Properties

Label 189618.bm
Number of curves $1$
Conductor $189618$
CM no
Rank $2$

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Show commands: SageMath
sage: E = EllipticCurve("bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.bm1 189618e1 \([1, 0, 0, -52699, 4965713]\) \(-95773342660124233/7719031406592\) \(-1304516307714048\) \([]\) \(1451520\) \(1.6468\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 189618.bm1 has rank \(2\).

Complex multiplication

The elliptic curves in class 189618.bm do not have complex multiplication.

Modular form 189618.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 2q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} - 2q^{10} - q^{11} + q^{12} - 2q^{14} - 2q^{15} + q^{16} + q^{17} + q^{18} - 8q^{19} + O(q^{20})\)  Toggle raw display