Properties

Label 137904cw
Number of curves $1$
Conductor $137904$
CM no
Rank $1$

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

Elliptic curves in class 137904cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
137904.j1 137904cw1 \([0, -1, 0, -166521, 26241669]\) \(-69842532158464/96702579\) \(-707052123857664\) \([]\) \(684288\) \(1.7536\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 137904cw1 has rank \(1\).

Complex multiplication

The elliptic curves in class 137904cw do not have complex multiplication.

Modular form 137904.2.a.cw

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} - 4 q^{11} + q^{15} - q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display