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	69696gk	Isogeny class
Conductor	69696	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	1474726323280674816 = 220 · 38 · 118	Discriminant
Eigenvalues	2- 3-  2 -4 11- -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1534764,729494480]	[a1,a2,a3,a4,a6]
Generators	[170:21760:1] [298:17280:1]	Generators of the group modulo torsion
j	1180932193/4356	j-invariant
L	10.596407899359	L(r)(E,1)/r!
Ω	0.27007008112214	Real period
R	9.8089427893715	Regulator
r	2	Rank of the group of rational points
S	0.99999999999683	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	69696cm2 17424bz2 23232de2 6336ci2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696gk2

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	-	-6	2	-4	4	-6	0	-6	-6	-4	-12	2	-12	-14	4	-12	6	-4	4	-10	-14

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Quadratic twists for elliptic curve 69696gk2

-4	8	-3	-11
69696cm2	17424bz2	23232de2	6336ci2

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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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