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	69696ex	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	1483416212078592 = 221 · 312 · 113	Discriminant
Eigenvalues	2- 3-  0  0 11+  6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-273900,-55143088]	[a1,a2,a3,a4,a6]
Generators	[988:25272:1]	Generators of the group modulo torsion
j	8934171875/5832	j-invariant
L	6.2155572867419	L(r)(E,1)/r!
Ω	0.20869813276846	Real period
R	3.722815583261	Regulator
r	1	Rank of the group of rational points
S	0.99999999996762	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696t2 17424bk2 23232cn2 69696ey2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ex2

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 69696ex2

-4	8	-3	-11
69696t2	17424bk2	23232cn2	69696ey2

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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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