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	12870x	Isogeny class
Conductor	12870	Conductor
∏ cp	512	Product of Tamagawa factors cp
Δ	9145194213870000 = 24 · 37 · 54 · 114 · 134	Discriminant
Eigenvalues	2+ 3- 5-  0 11- 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1443834,668110788]	[a1,a2,a3,a4,a6]
Generators	[-483:35634:1]	Generators of the group modulo torsion
j	456612868287073618849/12544848030000	j-invariant
L	3.8177889472885	L(r)(E,1)/r!
Ω	0.3816280088778	Real period
R	0.31262355442304	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	102960ea4 4290w3 64350ed4	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12870x4

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

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Quadratic twists for elliptic curve 12870x4

-4	-3	5
102960ea4	4290w3	64350ed4

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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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