Properties

Label 100011.a
Number of curves $1$
Conductor $100011$
CM no
Rank $1$

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

Elliptic curves in class 100011.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100011.a1 100011e1 \([0, 1, 1, 1070, 7408]\) \(135353378115584/99811078011\) \(-99811078011\) \([]\) \(121968\) \(0.79881\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100011.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100011.a do not have complex multiplication.

Modular form 100011.2.a.a

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