Properties

Label 111573.e
Number of curves $1$
Conductor $111573$
CM no
Rank $1$

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

Elliptic curves in class 111573.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
111573.e1 111573ba1 \([0, 0, 1, -399, 3064]\) \(196661248/253\) \(9037413\) \([]\) \(38160\) \(0.24237\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 111573.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 111573.e do not have complex multiplication.

Modular form 111573.2.a.e

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