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	27600p	Isogeny class
Conductor	27600	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-88320000 = -1 · 211 · 3 · 54 · 23	Discriminant
Eigenvalues	2+ 3+ 5-  3  0 -2 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-208,1312]	[a1,a2,a3,a4,a6]
Generators	[12:-20:1]	Generators of the group modulo torsion
j	-781250/69	j-invariant
L	4.7566570426434	L(r)(E,1)/r!
Ω	1.8699472554317	Real period
R	0.21197821796071	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13800bb1 110400jp1 82800bu1 27600x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600p1

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	0	-2	-3	-6	-	-3	-6	9	0	6	5	-12	6	10	-6	-15	3	16	15	13	-6

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Quadratic twists for elliptic curve 27600p1

-4	8	-3	5
13800bb1	110400jp1	82800bu1	27600x1

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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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