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	12870bw	Isogeny class
Conductor	12870	Conductor
∏ cp	288	Product of Tamagawa factors cp
Δ	-5157606480998400 = -1 · 212 · 37 · 52 · 116 · 13	Discriminant
Eigenvalues	2- 3- 5+  2 11- 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1277753,556257881]	[a1,a2,a3,a4,a6]
Generators	[-95:26062:1]	Generators of the group modulo torsion
j	-316472948332146183241/7074906009600	j-invariant
L	7.1206166468199	L(r)(E,1)/r!
Ω	0.39812541420898	Real period
R	2.2356700905943	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	102960di3 4290o3 64350bm3	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12870bw3

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

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Quadratic twists for elliptic curve 12870bw3

-4	-3	5
102960di3	4290o3	64350bm3

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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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