Properties

Label 20691.e
Number of curves $1$
Conductor $20691$
CM no
Rank $0$

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

Elliptic curves in class 20691.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20691.e1 20691s1 \([0, 0, 1, -2541, 54238]\) \(-1404928/171\) \(-220841022699\) \([]\) \(45760\) \(0.91171\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20691.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 20691.e do not have complex multiplication.

Modular form 20691.2.a.e

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