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	1638m	Isogeny class
Conductor	1638	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	4843277712 = 24 · 39 · 7 · 133	Discriminant
Eigenvalues	2- 3+  0 7-  0 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-8615,-305585]	[a1,a2,a3,a4,a6]
j	3592121380875/246064	j-invariant
L	2.9733272296676	L(r)(E,1)/r!
Ω	0.49555453827794	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	13104bf3 52416o3 1638c1 40950b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638m3

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

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Quadratic twists for elliptic curve 1638m3

-4	8	-3	5	-7	13
13104bf3	52416o3	1638c1	40950b3	11466bj3	21294a3

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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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