Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 11858.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11858.b1 11858t1 \([1, -1, 0, -51508, -7373360]\) \(-8773917273/8605184\) \(-14822420912262656\) \([]\) \(207360\) \(1.7988\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 11858.b1 has rank \(1\).

Complex multiplication

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

Modular form 11858.2.a.b

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