Cremona's table of elliptic curves

1298 = 2 · 11 · 59

Field	Data	Notes
Atkin-Lehner	2- 11+ 59-	Signs for the Atkin-Lehner involutions
Class	1298b	Isogeny class
Conductor	1298	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-119772545024 = -1 · 224 · 112 · 59	Discriminant
Eigenvalues	2-  1 -1 -3 11+ -4 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1106,21764]	[a1,a2,a3,a4,a6]
Generators	[-28:190:1]	Generators of the group modulo torsion
j	-149628263143969/119772545024	j-invariant
L	3.7631086945633	L(r)(E,1)/r!
Ω	0.96146397766818	Real period
R	0.081540338093102	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	10384d1 41536h1 11682g1 32450a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1298b1

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	-1	-3	+	-4	-2	-5	-2	3	10	4	9	6	-12	-13	-	8	-14	0	4	11	2	0	-10

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Quadratic twists for elliptic curve 1298b1

-4	8	-3	5	-7	-11	-59
10384d1	41536h1	11682g1	32450a1	63602n1	14278d1	76582b1

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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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