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	69696gr	Isogeny class
Conductor	69696	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-2788154454952525824 = -1 · 214 · 38 · 1110	Discriminant
Eigenvalues	2- 3-  3  2 11-  5 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-192031356,1024250861392]	[a1,a2,a3,a4,a6]
j	-2527934627152/9	j-invariant
L	5.4449235976483	L(r)(E,1)/r!
Ω	0.17015386219882	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69696dd2 17424cd2 23232ds2 69696gs2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696gr2

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
-	-	3	2	-	5	-3	4	6	9	-8	7	-3	10	12	-9	6	14	2	-6	10	8	0	3	-1

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Quadratic twists for elliptic curve 69696gr2

-4	8	-3	-11
69696dd2	17424cd2	23232ds2	69696gs2

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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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