Properties

Label 83391j
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 83391j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83391.a1 83391j1 \([0, -1, 1, -417436, -103669470]\) \(170990840664064/39501\) \(1858359345381\) \([]\) \(777600\) \(1.7345\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 83391.2.a.j

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