Properties

Label 58835n
Number of curves $1$
Conductor $58835$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 58835n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58835.a1 58835n1 \([0, 1, 1, -560, -125904]\) \(-4096/1435\) \(-6816399585835\) \([]\) \(188160\) \(1.1417\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 58835n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 58835n do not have complex multiplication.

Modular form 58835.2.a.n

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 4 q^{6} + q^{7} + q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} - 2 q^{14} - 2 q^{15} - 4 q^{16} + 4 q^{17} - 2 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display