Cremona's table of elliptic curves

16968 = 2³ · 3 · 7 · 101

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 101+	Signs for the Atkin-Lehner involutions
Class	16968b	Isogeny class
Conductor	16968	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	6704667648 = 210 · 33 · 74 · 101	Discriminant
Eigenvalues	2- 3+  2 7-  0 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-58192,-5383748]	[a1,a2,a3,a4,a6]
Generators	[475266:5837860:1331]	Generators of the group modulo torsion
j	21282422948152132/6547527	j-invariant
L	4.9284731310003	L(r)(E,1)/r!
Ω	0.30738531792306	Real period
R	8.0167673008928	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33936b4 50904e4 118776p4	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 16968b3

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

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Quadratic twists for elliptic curve 16968b3

-4	-3	-7
33936b4	50904e4	118776p4

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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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