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	69696es	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-189651018940416 = -1 · 215 · 33 · 118	Discriminant
Eigenvalues	2- 3+ -2 -4 11-  4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,10164,532400]	[a1,a2,a3,a4,a6]
Generators	[77:1331:1]	Generators of the group modulo torsion
j	74088/121	j-invariant
L	4.8223449489912	L(r)(E,1)/r!
Ω	0.38728708639047	Real period
R	1.5564503432402	Regulator
r	1	Rank of the group of rational points
S	1.000000000131	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696er2 34848f2 69696eo2 6336bt2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696es2

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

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Quadratic twists for elliptic curve 69696es2

-4	8	-3	-11
69696er2	34848f2	69696eo2	6336bt2

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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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