Cremona's table of elliptic curves

1653 = 3 · 19 · 29

Field	Data	Notes
Atkin-Lehner	3+ 19- 29+	Signs for the Atkin-Lehner involutions
Class	1653b	Isogeny class
Conductor	1653	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	11337927 = 3 · 194 · 29	Discriminant
Eigenvalues	1 3+ -2  0  0 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-471,-4134]	[a1,a2,a3,a4,a6]
j	11593815110137/11337927	j-invariant
L	1.0245893362538	L(r)(E,1)/r!
Ω	1.0245893362538	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	26448q4 105792r4 4959h4 41325k4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1653b3

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	0	0	-2	-2	-	0	+	8	10	6	-4	-4	10	4	14	0	-8	10	8	4	-10	14

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Quadratic twists for elliptic curve 1653b3

-4	8	-3	5	-7	-19	29
26448q4	105792r4	4959h4	41325k4	80997k4	31407f4	47937d4

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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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