Properties

Label 83582.c
Number of curves $1$
Conductor $83582$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 83582.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83582.c1 83582i1 \([1, 1, 0, -1862, -29912]\) \(4826809/316\) \(46779340924\) \([]\) \(95040\) \(0.79718\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 83582.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 83582.c do not have complex multiplication.

Modular form 83582.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 3 q^{7} - q^{8} - 2 q^{9} - q^{10} - 4 q^{11} - q^{12} - 7 q^{13} - 3 q^{14} - q^{15} + q^{16} + 4 q^{17} + 2 q^{18} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display