Properties

Label 8619.d
Number of curves $1$
Conductor $8619$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 8619.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8619.d1 8619c1 \([1, 1, 1, 142210, -108603682]\) \(2307174311/38336139\) \(-5284962305853631011\) \([]\) \(140400\) \(2.2732\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8619.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 8619.d do not have complex multiplication.

Modular form 8619.2.a.d

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