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	4	Product of Tamagawa factors cp
Δ	-428122517504 = -1 · 212 · 116 · 59	Discriminant
Eigenvalues	2+  1  3  5 11+ -4  6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,1808,-10562]	[a1,a2,a3,a4,a6]
j	654130263799943/428122517504	j-invariant
L	2.1512286685793	L(r)(E,1)/r!
Ω	0.53780716714483	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10384e2 41536i2 11682s2 32450o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1298a2

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 1298a2

-4	8	-3	5	-7	-11	-59
10384e2	41536i2	11682s2	32450o2	63602e2	14278h2	76582c2

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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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