Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 189618.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.bc1 189618q1 \([1, 1, 1, -1388, 19469]\) \(-1749947265625/14648832\) \(-2475652608\) \([]\) \(169344\) \(0.62861\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 189618.bc1 has rank \(2\).

Complex multiplication

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

Modular form 189618.2.a.bc

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