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	16	Product of Tamagawa factors cp
Δ	286152818688 = 215 · 38 · 113	Discriminant
Eigenvalues	2+ 3-  0 -4 11+  2 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4620,-118096]	[a1,a2,a3,a4,a6]
Generators	[-40:52:1] [-35:27:1]	Generators of the group modulo torsion
j	343000/9	j-invariant
L	9.6382947142166	L(r)(E,1)/r!
Ω	0.5800086068815	Real period
R	4.1543757282054	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	69696v2 34848k2 23232b2 69696w2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696x2

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 69696x2

-4	8	-3	-11
69696v2	34848k2	23232b2	69696w2

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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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