Properties

Label 100011c
Number of curves 1
Conductor 100011
CM no
Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("100011.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100011c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100011.e1 100011c1 [0, -1, 1, 9022524, -11690123677] [] 10765440 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100011c1 has rank \(1\).

Modular form 100011.2.a.e

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