Cremona's table of elliptic curves

4624 = 2⁴ · 17²

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	4624c	Isogeny class
Conductor	4624	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	5030912 = 210 · 173	Discriminant
Eigenvalues	2+ -2  0  2  2 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-368,2596]	[a1,a2,a3,a4,a6]
Generators	[-6:68:1]	Generators of the group modulo torsion
j	1098500	j-invariant
L	2.8103849595659	L(r)(E,1)/r!
Ω	2.4125268527471	Real period
R	0.58245672092018	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2312a2 18496m2 41616s2 115600h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4624c2

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	2	2	-2	+	4	-6	-8	6	8	0	-12	8	-6	4	-8	-4	6	8	2	-4	-14	8

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Quadratic twists for elliptic curve 4624c2

-4	8	-3	5	17
2312a2	18496m2	41616s2	115600h2	4624b2

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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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