Properties

Label 61050cp
Number of curves $1$
Conductor $61050$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 61050cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61050.cj1 61050cp1 \([1, 0, 0, 187, 1617]\) \(46268279/97680\) \(-1526250000\) \([]\) \(32256\) \(0.44648\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 61050cp1 has rank \(1\).

Complex multiplication

The elliptic curves in class 61050cp do not have complex multiplication.

Modular form 61050.2.a.cp

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 2 q^{7} + q^{8} + q^{9} + q^{11} + q^{12} + 2 q^{13} - 2 q^{14} + q^{16} + 3 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display