Properties

Label 416955cj
Number of curves $1$
Conductor $416955$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cj1")
 
E.isogeny_class()
 

Elliptic curves in class 416955cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
416955.cj1 416955cj1 \([0, -1, 1, -45606, -3745753]\) \(-222985990144/841995\) \(-39612396572595\) \([]\) \(2122848\) \(1.4686\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 416955cj1 has rank \(1\).

Complex multiplication

The elliptic curves in class 416955cj do not have complex multiplication.

Modular form 416955.2.a.cj

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - q^{7} + q^{9} - 2 q^{10} + q^{11} - 2 q^{12} + 2 q^{13} - 2 q^{14} + q^{15} - 4 q^{16} + q^{17} + 2 q^{18} + O(q^{20})\) Copy content Toggle raw display