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	1638n	Isogeny class
Conductor	1638	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-605409714 = -1 · 2 · 39 · 7 · 133	Discriminant
Eigenvalues	2- 3+  3 7-  3 13- -3  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-191,-1511]	[a1,a2,a3,a4,a6]
j	-38958219/30758	j-invariant
L	3.7278834478098	L(r)(E,1)/r!
Ω	0.6213139079683	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	13104bh2 52416w2 1638d1 40950c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638n2

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	5	-3	-3	-10	-7	6	5	0	6	6	-7	-4	-6	-1	-10	6	-6	2

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Quadratic twists for elliptic curve 1638n2

-4	8	-3	5	-7	13
13104bh2	52416w2	1638d1	40950c2	11466bm2	21294f2

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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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