Properties

Label 100022.b
Number of curves $1$
Conductor $100022$
CM no
Rank $1$

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

Elliptic curves in class 100022.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100022.b1 100022d1 \([1, 1, 0, -116, -520]\) \(174958262857/5201144\) \(5201144\) \([]\) \(44736\) \(0.065616\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100022.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100022.b do not have complex multiplication.

Modular form 100022.2.a.b

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