Cremona's table of elliptic curves

7098 = 2 · 3 · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	7098w	Isogeny class
Conductor	7098	Conductor
∏ cp	63	Product of Tamagawa factors cp
Δ	3282271469568 = 221 · 33 · 73 · 132	Discriminant
Eigenvalues	2- 3-  0 7+  3 13+ -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-10098,-381564]	[a1,a2,a3,a4,a6]
Generators	[-60:126:1]	Generators of the group modulo torsion
j	673822943613625/19421724672	j-invariant
L	7.1288200893885	L(r)(E,1)/r!
Ω	0.47709585771138	Real period
R	0.23717639255462	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	56784bv2 21294p2 49686bx2 7098n2	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 7098w2

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	+	3	+	-3	-5	-6	-9	-8	-8	-3	8	-3	-3	6	-7	-2	6	16	-13	-18	15	16

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Quadratic twists for elliptic curve 7098w2

-4	-3	-7	13
56784bv2	21294p2	49686bx2	7098n2

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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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