Properties

Label 100023.a
Number of curves $1$
Conductor $100023$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 100023.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100023.a1 100023d1 \([1, 0, 0, -287, 1764]\) \(2614953528433/132330429\) \(132330429\) \([]\) \(36096\) \(0.31675\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100023.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 100023.a do not have complex multiplication.

Modular form 100023.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - 3 q^{5} - q^{6} + q^{7} + 3 q^{8} + q^{9} + 3 q^{10} + q^{11} - q^{12} + q^{13} - q^{14} - 3 q^{15} - q^{16} - 3 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display