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	27600ba	Isogeny class
Conductor	27600	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	460800	Modular degree for the optimal curve
Δ	-8980614787500000000 = -1 · 28 · 310 · 511 · 233	Discriminant
Eigenvalues	2+ 3- 5+ -3  4  0 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,190367,-140529637]	[a1,a2,a3,a4,a6]
Generators	[638:15525:1]	Generators of the group modulo torsion
j	190737654201344/2245153696875	j-invariant
L	6.3587517464118	L(r)(E,1)/r!
Ω	0.11368990783492	Real period
R	0.93217769098217	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	13800b1 110400gs1 82800x1 5520c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 27600ba1

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	4	0	-3	4	-	1	-1	-1	3	-12	-10	9	9	-10	1	-5	0	-4	-9	-8	10

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Quadratic twists for elliptic curve 27600ba1

-4	8	-3	5
13800b1	110400gs1	82800x1	5520c1

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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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