Cremona's table of elliptic curves

12936 = 2³ · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	12936t	Isogeny class
Conductor	12936	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	515451795167232 = 211 · 34 · 710 · 11	Discriminant
Eigenvalues	2- 3+ -2 7- 11- -6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1863584,979821228]	[a1,a2,a3,a4,a6]
Generators	[-583:43218:1] [677:5292:1]	Generators of the group modulo torsion
j	2970658109581346/2139291	j-invariant
L	5.1806950683377	L(r)(E,1)/r!
Ω	0.43292934330202	Real period
R	5.9833032208257	Regulator
r	2	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25872q4 103488df4 38808v4 1848k3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12936t4

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	-6	0	-8	-2	-4	-2	2	-12	-12	6	-4	-6	4	0	2	8	0	6	-18

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Quadratic twists for elliptic curve 12936t4

-4	8	-3	-7
25872q4	103488df4	38808v4	1848k3

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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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