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	69696dx	Isogeny class
Conductor	69696	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4710334464 = 217 · 33 · 113	Discriminant
Eigenvalues	2- 3+ -2 -2 11+ -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5676,164560]	[a1,a2,a3,a4,a6]
Generators	[-54:560:1] [-22:528:1]	Generators of the group modulo torsion
j	4293378	j-invariant
L	8.8751683804153	L(r)(E,1)/r!
Ω	1.3369733944549	Real period
R	1.6595633872072	Regulator
r	2	Rank of the group of rational points
S	0.99999999999836	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696c2 17424b2 69696dv2 69696dw2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696dx2

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	-2	+	-2	-2	4	-6	-2	0	2	6	-8	-2	-10	-4	-14	-4	-6	8	2	-12	-8	-2

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Quadratic twists for elliptic curve 69696dx2

-4	8	-3	-11
69696c2	17424b2	69696dv2	69696dw2

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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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