Cremona's table of elliptic curves

7854 = 2 · 3 · 7 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11- 17-	Signs for the Atkin-Lehner involutions
Class	7854o	Isogeny class
Conductor	7854	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2210840757291012 = 22 · 3 · 74 · 11 · 178	Discriminant
Eigenvalues	2- 3- -2 7+ 11- -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1692044,-847298292]	[a1,a2,a3,a4,a6]
Generators	[-20292:11506:27]	Generators of the group modulo torsion
j	535745688862577855368897/2210840757291012	j-invariant
L	6.4921984580675	L(r)(E,1)/r!
Ω	0.13237218811224	Real period
R	6.1306292419248	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	62832bf6 23562h6 54978bq6 86394bh6	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7854o5

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	+	-	-2	-	-4	8	-2	0	-10	-6	4	-8	-10	4	-10	4	8	-14	16	4	-6	2

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Quadratic twists for elliptic curve 7854o5

-4	-3	-7	-11
62832bf6	23562h6	54978bq6	86394bh6

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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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