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	69696di	Isogeny class
Conductor	69696	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-28163176312651776 = -1 · 214 · 36 · 119	Discriminant
Eigenvalues	2+ 3- -3 -2 11- -4  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-336864,-75685984]	[a1,a2,a3,a4,a6]
Generators	[175662883:3323707981:205379]	Generators of the group modulo torsion
j	-199794688/1331	j-invariant
L	4.3742883442944	L(r)(E,1)/r!
Ω	0.099045111248549	Real period
R	11.041151575619	Regulator
r	1	Rank of the group of rational points
S	0.99999999995826	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69696gv2 4356h2 7744h2 6336r2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696di2

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	-	-4	6	8	3	0	5	1	0	-10	0	-6	3	-4	1	-15	4	-2	-6	9	-7

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Quadratic twists for elliptic curve 69696di2

-4	8	-3	-11
69696gv2	4356h2	7744h2	6336r2

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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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