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	-155309314694688 = -1 · 25 · 34 · 72 · 114 · 174	Discriminant
Eigenvalues	2- 3+ -2 7+ 11+  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,1806,-598113]	[a1,a2,a3,a4,a6]
Generators	[115:1013:1]	Generators of the group modulo torsion
j	651421248244703/155309314694688	j-invariant
L	4.5414536888697	L(r)(E,1)/r!
Ω	0.27137196649179	Real period
R	0.41837903778162	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	62832ca3 23562j3 54978bx3 86394j3	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7854k4

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 7854k4

-4	-3	-7	-11
62832ca3	23562j3	54978bx3	86394j3

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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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