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	1638f	Isogeny class
Conductor	1638	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	38080	Modular degree for the optimal curve
Δ	-543126557487661056 = -1 · 217 · 313 · 7 · 135	Discriminant
Eigenvalues	2+ 3- -3 7+ -1 13+ -7  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-904356,333142096]	[a1,a2,a3,a4,a6]
j	-112205650221491190337/745029571313664	j-invariant
L	0.58753816261883	L(r)(E,1)/r!
Ω	0.29376908130941	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	13104cf1 52416ce1 546e1 40950ek1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638f1

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	+	-1	+	-7	1	7	-3	0	-5	-4	11	0	14	-4	1	-6	12	5	-10	14	6	6

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Quadratic twists for elliptic curve 1638f1

-4	8	-3	5	-7	13
13104cf1	52416ce1	546e1	40950ek1	11466be1	21294cn1

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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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