Properties

Label 83391.j
Number of curves $1$
Conductor $83391$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 83391.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83391.j1 83391c1 \([0, -1, 1, -308775, 54677765]\) \(69203793903616/12699136989\) \(597442087587192309\) \([]\) \(950400\) \(2.1295\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83391.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 83391.j do not have complex multiplication.

Modular form 83391.2.a.j

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