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	32	Product of Tamagawa factors cp
Δ	4686403566265344 = 210 · 38 · 78 · 112	Discriminant
Eigenvalues	2- 3+ -2 7- 11- -6 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-117224,15131964]	[a1,a2,a3,a4,a6]
Generators	[-170:5488:1] [-2:3920:1]	Generators of the group modulo torsion
j	1478729816932/38900169	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	4	Number of elements in the torsion subgroup
Twists	25872q2 103488df2 38808v2 1848k2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12936t2

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 12936t2

-4	8	-3	-7
25872q2	103488df2	38808v2	1848k2

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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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