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	7098u	Isogeny class
Conductor	7098	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	20160	Modular degree for the optimal curve
Δ	-10460052286866 = -1 · 2 · 35 · 73 · 137	Discriminant
Eigenvalues	2- 3+  1 7-  1 13+ -1 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-18340,-976201]	[a1,a2,a3,a4,a6]
Generators	[1262:1731:8]	Generators of the group modulo torsion
j	-141339344329/2167074	j-invariant
L	5.7771311598003	L(r)(E,1)/r!
Ω	0.20493866259474	Real period
R	2.3491301765838	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	56784cl1 21294bf1 49686cz1 546a1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 7098u1

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
-	+	1	-	1	+	-1	-7	3	-3	-8	-7	-8	7	-8	-10	-4	7	-2	-4	1	2	6	-14	14

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Quadratic twists for elliptic curve 7098u1

-4	-3	-7	13
56784cl1	21294bf1	49686cz1	546a1

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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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