Properties

Label 100011b
Number of curves $1$
Conductor $100011$
CM no
Rank $1$

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

Elliptic curves in class 100011b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100011.b1 100011b1 \([1, 1, 1, 39, -2310]\) \(6549699311/2341157499\) \(-2341157499\) \([]\) \(41040\) \(0.47695\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100011b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100011b do not have complex multiplication.

Modular form 100011.2.a.b

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