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	7098n	Isogeny class
Conductor	7098	Conductor
∏ cp	27	Product of Tamagawa factors cp
deg	78624	Modular degree for the optimal curve
Δ	14386200892172928 = 27 · 39 · 7 · 138	Discriminant
Eigenvalues	2+ 3-  0 7- -3 13+ -3  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-223591,40263914]	[a1,a2,a3,a4,a6]
Generators	[-324:9034:1]	Generators of the group modulo torsion
j	1515434103625/17635968	j-invariant
L	3.6775224466551	L(r)(E,1)/r!
Ω	0.39696774883612	Real period
R	3.0880111020247	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	56784bd1 21294cj1 49686e1 7098w1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 7098n1

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 7098n1

-4	-3	-7	13
56784bd1	21294cj1	49686e1	7098w1

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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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