Cremona's table of elliptic curves

1098 = 2 · 3² · 61

Field	Data	Notes
Atkin-Lehner	2- 3- 61+	Signs for the Atkin-Lehner involutions
Class	1098j	Isogeny class
Conductor	1098	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-711504 = -1 · 24 · 36 · 61	Discriminant
Eigenvalues	2- 3- -1 -5  3 -3  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,22,-7]	[a1,a2,a3,a4,a6]
Generators	[3:7:1]	Generators of the group modulo torsion
j	1685159/976	j-invariant
L	3.1674557478253	L(r)(E,1)/r!
Ω	1.6996525301653	Real period
R	0.23294877126425	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	8784q1 35136v1 122a1 27450r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1098j1

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	-5	3	-3	0	0	-5	-6	0	-12	3	-8	-12	2	9	+	7	16	-3	1	12	-12	2

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Quadratic twists for elliptic curve 1098j1

-4	8	-3	5	-7	61
8784q1	35136v1	122a1	27450r1	53802cg1	66978e1

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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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