Cremona's table of elliptic curves

27508 = 2² · 13 · 23²

Field	Data	Notes
Atkin-Lehner	2- 13+ 23-	Signs for the Atkin-Lehner involutions
Class	27508b	Isogeny class
Conductor	27508	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-6404624701696 = -1 · 28 · 132 · 236	Discriminant
Eigenvalues	2-  0 -2  2  2 13+ -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,529,121670]	[a1,a2,a3,a4,a6]
Generators	[29334:967148:27]	Generators of the group modulo torsion
j	432/169	j-invariant
L	4.6360956546662	L(r)(E,1)/r!
Ω	0.58432303608868	Real period
R	7.9341312396292	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	110032g2 52a1	Quadratic twists by: -4 -23

Hecke Eigenvalues for elliptic curve 27508b2

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
-	0	-2	2	2	+	-6	6	-	2	10	6	-6	-4	-2	-6	-10	2	-10	10	2	4	6	6	-2

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Quadratic twists for elliptic curve 27508b2

-4	-23
110032g2	52a1

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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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