Cremona's table of elliptic curves

3146 = 2 · 11² · 13

Field	Data	Notes
Atkin-Lehner	2+ 11- 13-	Signs for the Atkin-Lehner involutions
Class	3146g	Isogeny class
Conductor	3146	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	6443008 = 212 · 112 · 13	Discriminant
Eigenvalues	2+ -1  2  2 11- 13-  1 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-134,532]	[a1,a2,a3,a4,a6]
Generators	[-4:34:1]	Generators of the group modulo torsion
j	2224882033/53248	j-invariant
L	2.5104487296397	L(r)(E,1)/r!
Ω	2.373388698618	Real period
R	0.52887433295303	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25168bi1 100672k1 28314cf1 78650bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3146g1

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
+	-1	2	2	-	-	1	-2	-5	-1	-6	-2	2	-5	2	-13	-4	5	-10	6	4	1	-12	-10	-10

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Quadratic twists for elliptic curve 3146g1

-4	8	-3	5	-11	13
25168bi1	100672k1	28314cf1	78650bt1	3146m1	40898bk1

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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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