Properties

Label 1083.e
Number of curves $1$
Conductor $1083$
CM no
Rank $1$

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

Elliptic curves in class 1083.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1083.e1 1083e1 \([0, 1, 1, -842, -10633]\) \(-1404928/171\) \(-8044845651\) \([]\) \(1440\) \(0.63567\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1083.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1083.e do not have complex multiplication.

Modular form 1083.2.a.e

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