Properties

Label 20570.e
Number of curves $1$
Conductor $20570$
CM no
Rank $1$

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

Elliptic curves in class 20570.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20570.e1 20570c1 \([1, 0, 1, 602, 7258]\) \(13651919/20570\) \(-36441009770\) \([]\) \(15360\) \(0.71196\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20570.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 20570.e do not have complex multiplication.

Modular form 20570.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 4 q^{7} - q^{8} - 2 q^{9} - q^{10} + q^{12} + q^{13} + 4 q^{14} + q^{15} + q^{16} - q^{17} + 2 q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display