Properties

Label 2093e
Number of curves $1$
Conductor $2093$
CM no
Rank $1$

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

Elliptic curves in class 2093e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2093.a1 2093e1 \([0, -1, 1, -42, 120]\) \(-8390176768/14651\) \(-14651\) \([]\) \(272\) \(-0.30699\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2093e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2093e do not have complex multiplication.

Modular form 2093.2.a.e

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