Cremona's table of elliptic curves

69696 = 2⁶ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11-	Signs for the Atkin-Lehner involutions
Class	69696ck	Isogeny class
Conductor	69696	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1244300335268069376 = 215 · 311 · 118	Discriminant
Eigenvalues	2+ 3-  2  4 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1366182444,-19436191250960]	[a1,a2,a3,a4,a6]
Generators	[-32097001525265800415924011791403823078410625179687184413384700:12893262384058556139055222379821834932159536355000510903432:1504079538642151498547805631079364688557546128445237453125]	Generators of the group modulo torsion
j	6663712298552914184/29403	j-invariant
L	8.9564521138483	L(r)(E,1)/r!
Ω	0.024832610669582	Real period
R	90.168249255916	Regulator
r	1	Rank of the group of rational points
S	0.99999999996965	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696cn4 34848cf4 23232cf4 6336bb3	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ck4

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	4	-	-2	2	-4	0	6	-4	2	-6	4	-8	-6	-12	-10	4	0	-10	12	12	-10	18

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Quadratic twists for elliptic curve 69696ck4

-4	8	-3	-11
69696cn4	34848cf4	23232cf4	6336bb3

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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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