Cremona's table of elliptic curves

4624 = 2⁴ · 17²

Field	Data	Notes
Atkin-Lehner	2- 17+	Signs for the Atkin-Lehner involutions
Class	4624f	Isogeny class
Conductor	4624	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4772841367386202112 = 213 · 1712	Discriminant
Eigenvalues	2- -2  0 -4  6  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-522608,100312660]	[a1,a2,a3,a4,a6]
j	159661140625/48275138	j-invariant
L	0.90425772548244	L(r)(E,1)/r!
Ω	0.22606443137061	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	578a4 18496n4 41616ca4 115600bz4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4624f4

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
-	-2	0	-4	6	2	+	4	0	0	-4	4	-6	-8	0	-6	0	4	-8	0	-2	8	0	-6	-14

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Quadratic twists for elliptic curve 4624f4

-4	8	-3	5	17
578a4	18496n4	41616ca4	115600bz4	272d4

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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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