Properties

Label 224175.cw
Number of curves 11
Conductor 224175224175
CM no
Rank 00

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 224175.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
224175.cw1 224175de1 [0,1,1,642,4493][0, -1, 1, 642, 4493] 5451776/49415451776/4941 26480671875-26480671875 [][] 245760245760 0.687310.68731 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 224175.cw1 has rank 00.

Complex multiplication

The elliptic curves in class 224175.cw do not have complex multiplication.

Modular form 224175.2.a.cw

sage: E.q_eigenform(10)
 
q+2q2q3+2q42q6+q92q124q16+5q17+2q18+6q19+O(q20)q + 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{6} + q^{9} - 2 q^{12} - 4 q^{16} + 5 q^{17} + 2 q^{18} + 6 q^{19} + O(q^{20}) Copy content Toggle raw display