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	10608p	Isogeny class
Conductor	10608	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4985929728 = 214 · 34 · 13 · 172	Discriminant
Eigenvalues	2- 3+  0  2  2 13+ 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4488,-114192]	[a1,a2,a3,a4,a6]
Generators	[-38:6:1]	Generators of the group modulo torsion
j	2441288319625/1217268	j-invariant
L	4.2412070401078	L(r)(E,1)/r!
Ω	0.58329905901594	Real period
R	1.8177669647123	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	1326c2 42432cl2 31824s2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 10608p2

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	2	-8	0	4	0	-6	0	2	-4	10	-12	-8	-12	-6	-16

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Quadratic twists for elliptic curve 10608p2

-4	8	-3
1326c2	42432cl2	31824s2

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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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