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	69696fx	Isogeny class
Conductor	69696	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	115200	Modular degree for the optimal curve
Δ	-909193450176 = -1 · 26 · 36 · 117	Discriminant
Eigenvalues	2- 3-  1  4 11- -2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12342,529738]	[a1,a2,a3,a4,a6]
j	-2515456/11	j-invariant
L	3.5583726450176	L(r)(E,1)/r!
Ω	0.88959316506431	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69696fy1 34848r1 7744w1 6336by1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696fx1

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
-	-	1	4	-	-2	0	2	9	-4	-5	9	2	6	-4	-6	5	0	-13	-1	-14	-10	14	13	-19

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Quadratic twists for elliptic curve 69696fx1

-4	8	-3	-11
69696fy1	34848r1	7744w1	6336by1

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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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