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	27840ce	Isogeny class
Conductor	27840	Conductor
∏ cp	480	Product of Tamagawa factors cp
Δ	-392376960000000000 = -1 · 216 · 36 · 510 · 292	Discriminant
Eigenvalues	2+ 3- 5- -2 -6 -6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-58625,30609375]	[a1,a2,a3,a4,a6]
Generators	[-317:4176:1] [-275:5100:1]	Generators of the group modulo torsion
j	-340016315288836/5987197265625	j-invariant
L	9.0964307599614	L(r)(E,1)/r!
Ω	0.25310880789963	Real period
R	0.29949012954307	Regulator
r	2	Rank of the group of rational points
S	0.99999999999989	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27840de2 3480m2 83520z2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 27840ce2

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

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Quadratic twists for elliptic curve 27840ce2

-4	8	-3
27840de2	3480m2	83520z2

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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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