Cremona's table of elliptic curves

1638 = 2 · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	1638q	Isogeny class
Conductor	1638	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-5399043829452 = -1 · 22 · 39 · 74 · 134	Discriminant
Eigenvalues	2- 3-  2 7+  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,3631,-74419]	[a1,a2,a3,a4,a6]
j	7264187703863/7406095788	j-invariant
L	3.315613366674	L(r)(E,1)/r!
Ω	0.41445167083425	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	13104ck4 52416bq3 546c4 40950bl3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638q4

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
-	-	2	+	4	-	2	-4	4	2	0	-2	-2	4	12	-6	0	-10	4	8	-6	8	-8	6	2

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Quadratic twists for elliptic curve 1638q4

-4	8	-3	5	-7	13
13104ck4	52416bq3	546c4	40950bl3	11466cb4	21294bi3

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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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