Cremona's table of elliptic curves

27360 = 2⁵ · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 19+	Signs for the Atkin-Lehner involutions
Class	27360a	Isogeny class
Conductor	27360	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-77976000 = -1 · 26 · 33 · 53 · 192	Discriminant
Eigenvalues	2+ 3+ 5+ -4  4  2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,87,288]	[a1,a2,a3,a4,a6]
Generators	[3:24:1]	Generators of the group modulo torsion
j	42144192/45125	j-invariant
L	4.2154122010828	L(r)(E,1)/r!
Ω	1.2801479875063	Real period
R	1.6464550357549	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	27360c1 54720dh1 27360s1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 27360a1

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
+	+	+	-4	4	2	-6	+	0	0	-4	2	6	2	-4	6	2	10	-8	4	-14	16	-12	-14	0

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Quadratic twists for elliptic curve 27360a1

-4	8	-3
27360c1	54720dh1	27360s1

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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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