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	69696ey	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	2433024	Modular degree for the optimal curve
Δ	7.786554986922E+20	Discriminant
Eigenvalues	2- 3-  0  0 11+ -6  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2475660,667395344]	[a1,a2,a3,a4,a6]
Generators	[-827:46359:1]	Generators of the group modulo torsion
j	3723875/1728	j-invariant
L	6.5207629220659	L(r)(E,1)/r!
Ω	0.14262628008348	Real period
R	5.7149030653841	Regulator
r	1	Rank of the group of rational points
S	1.0000000000059	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696u1 17424bj1 23232co1 69696ex1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ey1

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

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Quadratic twists for elliptic curve 69696ey1

-4	8	-3	-11
69696u1	17424bj1	23232co1	69696ex1

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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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