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	2	Product of Tamagawa factors cp
Δ	40315017 = 3 · 19 · 294	Discriminant
Eigenvalues	1 3+ -2  0  0 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-321,2064]	[a1,a2,a3,a4,a6]
j	3675793187737/40315017	j-invariant
L	1.0245893362538	L(r)(E,1)/r!
Ω	2.0491786725076	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	26448q3 105792r3 4959h3 41325k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1653b4

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 1653b4

-4	8	-3	5	-7	-19	29
26448q3	105792r3	4959h3	41325k3	80997k3	31407f3	47937d3

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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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