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	27600cp	Isogeny class
Conductor	27600	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1343236800000000 = 212 · 3 · 58 · 234	Discriminant
Eigenvalues	2- 3- 5+  4  4  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-164408,25543188]	[a1,a2,a3,a4,a6]
Generators	[93996:366834:343]	Generators of the group modulo torsion
j	7679186557489/20988075	j-invariant
L	8.0396939926806	L(r)(E,1)/r!
Ω	0.48338425705822	Real period
R	8.3160486458626	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1725d3 110400ga4 82800er4 5520p4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600cp4

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	2	-6	-8	+	6	-8	-6	-6	-8	-8	-2	4	-10	8	0	6	4	-12	6	14

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Quadratic twists for elliptic curve 27600cp4

-4	8	-3	5
1725d3	110400ga4	82800er4	5520p4

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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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