Properties

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

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

Elliptic curves in class 8619.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8619.c1 8619l1 \([0, 1, 1, -4, 4]\) \(-53248/51\) \(-8619\) \([]\) \(912\) \(-0.54865\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 8619.c1 has rank \(1\).

Complex multiplication

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

Modular form 8619.2.a.c

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