Properties

Label 58835.k
Number of curves $1$
Conductor $58835$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 58835.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58835.k1 58835d1 \([0, 0, 1, -36734893, -560830904991]\) \(-408433618944/9886633715\) \(-132704916080711369514799715\) \([]\) \(61296312\) \(3.6932\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 58835.k1 has rank \(1\).

Complex multiplication

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

Modular form 58835.2.a.k

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - 3 q^{3} + 2 q^{4} - q^{5} - 6 q^{6} - q^{7} + 6 q^{9} - 2 q^{10} + q^{11} - 6 q^{12} - 7 q^{13} - 2 q^{14} + 3 q^{15} - 4 q^{16} + 2 q^{17} + 12 q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display