Cremona's table of elliptic curves

5185 = 5 · 17 · 61

Field	Data	Notes
Atkin-Lehner	5- 17- 61-	Signs for the Atkin-Lehner involutions
Class	5185a	Isogeny class
Conductor	5185	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	88145 = 5 · 172 · 61	Discriminant
Eigenvalues	-1  0 5-  0  0  6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1837,30756]	[a1,a2,a3,a4,a6]
j	685219199317281/88145	j-invariant
L	1.3216625972038	L(r)(E,1)/r!
Ω	2.6433251944077	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	82960e1 46665c1 25925a1 88145a1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5185a1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	0	-	0	0	6	-	4	8	-2	-4	6	-6	4	12	6	0	-	-12	-12	2	-4	0	-6	-6

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Quadratic twists for elliptic curve 5185a1

-4	-3	5	17
82960e1	46665c1	25925a1	88145a1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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