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	7098bf	Isogeny class
Conductor	7098	Conductor
∏ cp	858	Product of Tamagawa factors cp
deg	41184	Modular degree for the optimal curve
Δ	-1093573361147904 = -1 · 213 · 311 · 73 · 133	Discriminant
Eigenvalues	2- 3- -1 7- -3 13- -7  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-46381,4157009]	[a1,a2,a3,a4,a6]
Generators	[170:1007:1]	Generators of the group modulo torsion
j	-5022437771811277/497757560832	j-invariant
L	6.8270529773819	L(r)(E,1)/r!
Ω	0.47825509653854	Real period
R	0.016637435250908	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	56784bp1 21294bl1 49686co1 7098m1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 7098bf1

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	-	-3	-	-7	3	-1	-1	-8	1	4	5	0	-6	-10	-13	-8	6	13	-12	2	-12	6

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Quadratic twists for elliptic curve 7098bf1

-4	-3	-7	13
56784bp1	21294bl1	49686co1	7098m1

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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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