Properties

Label 11858.n
Number of curves $1$
Conductor $11858$
CM no
Rank $1$

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

Elliptic curves in class 11858.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11858.n1 11858l1 \([1, 0, 1, 17663, -27590]\) \(24167/14\) \(-353067511870766\) \([]\) \(50688\) \(1.4809\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 11858.n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 11858.n do not have complex multiplication.

Modular form 11858.2.a.n

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