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	7098k	Isogeny class
Conductor	7098	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	21083501712 = 24 · 3 · 7 · 137	Discriminant
Eigenvalues	2+ 3- -2 7+  4 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1187,-14194]	[a1,a2,a3,a4,a6]
j	38272753/4368	j-invariant
L	1.6389900099314	L(r)(E,1)/r!
Ω	0.81949500496571	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	56784cb1 21294cg1 49686k1 546g1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 7098k1

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	+	4	+	6	4	0	-6	8	-10	6	4	-4	10	-4	-6	8	0	10	-8	-4	6	2

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Quadratic twists for elliptic curve 7098k1

-4	-3	-7	13
56784cb1	21294cg1	49686k1	546g1

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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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