Cremona's table of elliptic curves

27040 = 2⁵ · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	27040c	Isogeny class
Conductor	27040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	12549703400000000 = 29 · 58 · 137	Discriminant
Eigenvalues	2+  0 5+ -4 -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-58643,-909558]	[a1,a2,a3,a4,a6]
Generators	[-7434:203286:343]	Generators of the group modulo torsion
j	9024895368/5078125	j-invariant
L	3.0989565126841	L(r)(E,1)/r!
Ω	0.33017705959231	Real period
R	9.3857414458489	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	27040b3 54080cv3 2080e2	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 27040c3

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

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Quadratic twists for elliptic curve 27040c3

-4	8	13
27040b3	54080cv3	2080e2

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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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