Properties

Label 100029.b
Number of curves $1$
Conductor $100029$
CM no
Rank $1$

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

Elliptic curves in class 100029.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100029.b1 100029a1 \([0, -1, 1, -64, 165]\) \(29446377472/8102349\) \(8102349\) \([]\) \(35160\) \(0.033195\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100029.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100029.b do not have complex multiplication.

Modular form 100029.2.a.b

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