Properties

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

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

Elliptic curves in class 100011.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100011.e1 100011c1 \([0, -1, 1, 9022524, -11690123677]\) \(81228381874428716689043456/106013477073021185065059\) \(-106013477073021185065059\) \([]\) \(10765440\) \(3.1040\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100011.e1 has rank \(1\).

Complex multiplication

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

Modular form 100011.2.a.e

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