Properties

Label 20286a
Number of curves $1$
Conductor $20286$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 20286a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20286.m1 20286a1 \([1, -1, 0, -1920, -32768]\) \(-12078102267/376832\) \(-24428888064\) \([]\) \(24192\) \(0.76994\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 20286a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 20286a do not have complex multiplication.

Modular form 20286.2.a.a

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