Properties

Label 289578.b
Number of curves $1$
Conductor $289578$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 289578.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289578.b1 289578b1 \([1, 1, 0, -943157, 352666053]\) \(-3843995587427449/6390046584\) \(-154240190334514296\) \([]\) \(4967424\) \(2.1940\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 289578.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 289578.b do not have complex multiplication.

Modular form 289578.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - 2 q^{11} - q^{12} - 6 q^{13} - q^{14} - q^{15} + q^{16} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display