Properties

Label 100023.e
Number of curves $1$
Conductor $100023$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 100023.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100023.e1 100023a1 \([0, -1, 1, -672, 7841]\) \(-33610706587648/5614591059\) \(-5614591059\) \([]\) \(99456\) \(0.59771\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100023.e1 has rank \(0\).

Complex multiplication

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

Modular form 100023.2.a.e

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