Cremona's table of elliptic curves

27600 = 2⁴ · 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 23+	Signs for the Atkin-Lehner involutions
Class	27600cq	Isogeny class
Conductor	27600	Conductor
∏ cp	320	Product of Tamagawa factors cp
Δ	3.1236921E+19	Discriminant
Eigenvalues	2- 3- 5+  4 -4 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-875408,-164848812]	[a1,a2,a3,a4,a6]
Generators	[-638:11592:1]	Generators of the group modulo torsion
j	1159246431432649/488076890625	j-invariant
L	7.1664180412337	L(r)(E,1)/r!
Ω	0.16205552282588	Real period
R	2.2110996022436	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1725g2 110400fy2 82800eq2 5520q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600cq2

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
-	-	+	4	-4	-6	2	4	+	-10	8	-2	2	-8	0	6	0	6	8	4	-10	-16	-12	-10	10

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Quadratic twists for elliptic curve 27600cq2

-4	8	-3	5
1725g2	110400fy2	82800eq2	5520q2

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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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