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	7854k	Isogeny class
Conductor	7854	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	773780603904 = 210 · 32 · 74 · 112 · 172	Discriminant
Eigenvalues	2- 3+ -2 7+ 11+  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-6034,-177889]	[a1,a2,a3,a4,a6]
Generators	[-47:91:1]	Generators of the group modulo torsion
j	24296523029999137/773780603904	j-invariant
L	4.5414536888697	L(r)(E,1)/r!
Ω	0.54274393298358	Real period
R	0.83675807556324	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	62832ca2 23562j2 54978bx2 86394j2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7854k2

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	0	10	-4	2	10	4	-12	-6	4	-10	12	-8	10	0	-12	-14	18

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Quadratic twists for elliptic curve 7854k2

-4	-3	-7	-11
62832ca2	23562j2	54978bx2	86394j2

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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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