Properties

Label 249690b
Number of curves 11
Conductor 249690249690
CM no
Rank 00

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

Elliptic curves in class 249690b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249690.b1 249690b1 [1,1,0,122503,15753973][1, 1, 0, -122503, 15753973] 203315001724620866809/9746178390466560203315001724620866809/9746178390466560 97461783904665609746178390466560 [][] 21548802154880 1.82821.8282 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 249690b1 has rank 00.

Complex multiplication

The elliptic curves in class 249690b do not have complex multiplication.

Modular form 249690.2.a.b

sage: E.q_eigenform(10)
 
qq2q3+q4q5+q6q7q8+q9+q103q11q12q13+q14+q15+q16q18q19+O(q20)q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - 3 q^{11} - q^{12} - q^{13} + q^{14} + q^{15} + q^{16} - q^{18} - q^{19} + O(q^{20}) Copy content Toggle raw display