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	69696x	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	11923034112 = 212 · 37 · 113	Discriminant
Eigenvalues	2+ 3-  0 -4 11+  2 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-660,3872]	[a1,a2,a3,a4,a6]
Generators	[34:-144:1] [-22:88:1]	Generators of the group modulo torsion
j	8000/3	j-invariant
L	9.6382947142166	L(r)(E,1)/r!
Ω	1.160017213763	Real period
R	1.0385939320513	Regulator
r	2	Rank of the group of rational points
S	0.9999999999898	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696v1 34848k1 23232b1 69696w1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696x1

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	-4	+	2	-2	-2	-6	2	-8	2	-6	-2	-6	4	4	10	-12	-10	-12	-8	-8	-2	-10

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Quadratic twists for elliptic curve 69696x1

-4	8	-3	-11
69696v1	34848k1	23232b1	69696w1

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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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