Cremona's table of elliptic curves

27840 = 2⁶ · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 29+	Signs for the Atkin-Lehner involutions
Class	27840bw	Isogeny class
Conductor	27840	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	-11300456448000 = -1 · 214 · 38 · 53 · 292	Discriminant
Eigenvalues	2+ 3- 5-  0  6 -6  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-465,-161937]	[a1,a2,a3,a4,a6]
Generators	[111:-1080:1]	Generators of the group modulo torsion
j	-680136784/689725125	j-invariant
L	7.5268458993954	L(r)(E,1)/r!
Ω	0.32373796850373	Real period
R	0.4843710186219	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	27840cv2 1740a2 83520bf2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 27840bw2

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	6	-6	4	-2	-8	+	-2	0	-2	0	0	14	-4	-6	12	-12	-16	-2	-12	-2	-12

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Quadratic twists for elliptic curve 27840bw2

-4	8	-3
27840cv2	1740a2	83520bf2

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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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