Cremona's table of elliptic curves

12870 = 2 · 3² · 5 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 11+ 13+	Signs for the Atkin-Lehner involutions
Class	12870by	Isogeny class
Conductor	12870	Conductor
∏ cp	176	Product of Tamagawa factors cp
Δ	3.2825200092827E+21	Discriminant
Eigenvalues	2- 3- 5-  0 11+ 13+ -6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3271113797,-72008980186179]	[a1,a2,a3,a4,a6]
j	5309860874757074224246393258249/4502770931800627200	j-invariant
L	3.5134866630043	L(r)(E,1)/r!
Ω	0.019962992403434	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	102960el4 4290b3 64350be4	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12870by3

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

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Quadratic twists for elliptic curve 12870by3

-4	-3	5
102960el4	4290b3	64350be4

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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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