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	69696cn	Isogeny class
Conductor	69696	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-1.785434979083E+25	Discriminant
Eigenvalues	2+ 3-  2 -4 11- -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-80117004,342804118448]	[a1,a2,a3,a4,a6]
Generators	[44869:9331641:1]	Generators of the group modulo torsion
j	-1343891598641864/421900912521	j-invariant
L	6.3367694873438	L(r)(E,1)/r!
Ω	0.065319254780223	Real period
R	6.0632671675528	Regulator
r	1	Rank of the group of rational points
S	1.0000000001036	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696ck3 34848bb2 23232v3 6336n4	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696cn3

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	-	-2	2	4	0	6	4	2	-6	-4	8	-6	12	-10	-4	0	-10	-12	-12	-10	18

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Quadratic twists for elliptic curve 69696cn3

-4	8	-3	-11
69696ck3	34848bb2	23232v3	6336n4

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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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