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	10608r	Isogeny class
Conductor	10608	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-491735839226112 = -1 · 28 · 34 · 136 · 173	Discriminant
Eigenvalues	2- 3+  0  4  0 13- 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,19612,137676]	[a1,a2,a3,a4,a6]
Generators	[825:24024:1]	Generators of the group modulo torsion
j	3258571509326000/1920843121977	j-invariant
L	4.4538141049449	L(r)(E,1)/r!
Ω	0.31854985952058	Real period
R	4.6605096730623	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	2652f4 42432cd4 31824bm4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 10608r4

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	4	0	-	+	-2	0	6	-8	8	0	-8	-6	-6	6	-10	-2	-12	-4	-8	-18	6	8

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Quadratic twists for elliptic curve 10608r4

-4	8	-3
2652f4	42432cd4	31824bm4

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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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