Properties

Label 29760cw
Number of curves $1$
Conductor $29760$
CM no
Rank $1$

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

Elliptic curves in class 29760cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29760.cq1 29760cw1 \([0, 1, 0, -665647905, -6850171784097]\) \(-124427822010671478697670089/5317924709672681472000\) \(-1394062055092435411795968000\) \([]\) \(17487360\) \(3.9746\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 29760cw1 has rank \(1\).

Complex multiplication

The elliptic curves in class 29760cw do not have complex multiplication.

Modular form 29760.2.a.cw

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} + 5 q^{11} - 2 q^{13} + q^{15} - 4 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display