Cremona's table of elliptic curves

10608 = 2⁴ · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+ 17-	Signs for the Atkin-Lehner involutions
Class	10608g	Isogeny class
Conductor	10608	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	2108176048862208 = 210 · 38 · 13 · 176	Discriminant
Eigenvalues	2+ 3-  0 -2  2 13+ 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-132928,18478532]	[a1,a2,a3,a4,a6]
Generators	[38:3672:1]	Generators of the group modulo torsion
j	253674278705546500/2058765672717	j-invariant
L	5.223820039901	L(r)(E,1)/r!
Ω	0.46643756874038	Real period
R	0.23332079458886	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	5304b2 42432bw2 31824b2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 10608g2

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
+	-	0	-2	2	+	-	4	-4	-2	-10	4	0	4	4	10	-4	10	4	-14	-16	-8	0	6	4

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Quadratic twists for elliptic curve 10608g2

-4	8	-3
5304b2	42432bw2	31824b2

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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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