Properties

Label 100014.a
Number of curves $1$
Conductor $100014$
CM no
Rank $0$

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

Elliptic curves in class 100014.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100014.a1 100014a1 \([1, 1, 0, 20239, 521685]\) \(916763542913931623/644335288713216\) \(-644335288713216\) \([]\) \(520704\) \(1.5301\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100014.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 100014.a do not have complex multiplication.

Modular form 100014.2.a.a

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