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	1098i	Isogeny class
Conductor	1098	Conductor
∏ cp	76	Product of Tamagawa factors cp
deg	1824	Modular degree for the optimal curve
Δ	-629493202944 = -1 · 219 · 39 · 61	Discriminant
Eigenvalues	2- 3- -1 -2 -6  0 -3  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-8213,291053]	[a1,a2,a3,a4,a6]
Generators	[159:-1808:1]	Generators of the group modulo torsion
j	-84033427451401/863502336	j-invariant
L	3.2241762809332	L(r)(E,1)/r!
Ω	0.91680713328739	Real period
R	0.046272951613526	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	8784p1 35136u1 366c1 27450p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1098i1

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	-2	-6	0	-3	0	1	-6	0	3	-12	1	12	2	0	+	4	13	-9	-14	-3	9	-1

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Quadratic twists for elliptic curve 1098i1

-4	8	-3	5	-7	61
8784p1	35136u1	366c1	27450p1	53802ch1	66978d1

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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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