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	1298a	Isogeny class
Conductor	1298	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	992	Modular degree for the optimal curve
Δ	-397613744 = -1 · 24 · 112 · 593	Discriminant
Eigenvalues	2+  1  3  5 11+ -4  6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-257,1828]	[a1,a2,a3,a4,a6]
j	-1866773548297/397613744	j-invariant
L	2.1512286685793	L(r)(E,1)/r!
Ω	1.6134215014345	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	10384e1 41536i1 11682s1 32450o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1298a1

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	5	+	-4	6	-1	6	3	2	8	-3	-10	-12	-9	-	-4	14	0	-4	11	-18	12	2

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Quadratic twists for elliptic curve 1298a1

-4	8	-3	5	-7	-11	-59
10384e1	41536i1	11682s1	32450o1	63602e1	14278h1	76582c1

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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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