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	1098a	Isogeny class
Conductor	1098	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-2401326 = -1 · 2 · 39 · 61	Discriminant
Eigenvalues	2+ 3+  1  4 -6 -6 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-69,251]	[a1,a2,a3,a4,a6]
Generators	[1:13:1]	Generators of the group modulo torsion
j	-1860867/122	j-invariant
L	2.0829307864499	L(r)(E,1)/r!
Ω	2.540500410405	Real period
R	0.4099449812956	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	8784i1 35136h1 1098g1 27450bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1098a1

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	4	-6	-6	-3	-6	-7	0	6	-3	0	7	-6	10	-6	+	4	-7	3	-2	15	9	-13

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Quadratic twists for elliptic curve 1098a1

-4	8	-3	5	-7	61
8784i1	35136h1	1098g1	27450bf1	53802g1	66978j1

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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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