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	1638t	Isogeny class
Conductor	1638	Conductor
∏ cp	108	Product of Tamagawa factors cp
Δ	-26711609573376 = -1 · 227 · 37 · 7 · 13	Discriminant
Eigenvalues	2- 3- -3 7- -3 13-  3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-234509,43769909]	[a1,a2,a3,a4,a6]
Generators	[207:1912:1]	Generators of the group modulo torsion
j	-1956469094246217097/36641439744	j-invariant
L	3.5793626035194	L(r)(E,1)/r!
Ω	0.61437641127669	Real period
R	0.48550076383974	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	13104by3 52416cq3 546d3 40950w3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638t3

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
-	-	-3	-	-3	-	3	-7	-9	9	-4	-7	-12	-1	0	6	-12	-1	14	-12	-7	-10	6	6	-10

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Quadratic twists for elliptic curve 1638t3

-4	8	-3	5	-7	13
13104by3	52416cq3	546d3	40950w3	11466cc3	21294t3

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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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