Cremona's table of elliptic curves

21360 = 2⁴ · 3 · 5 · 89

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 89+	Signs for the Atkin-Lehner involutions
Class	21360a	Isogeny class
Conductor	21360	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	163840	Modular degree for the optimal curve
Δ	5839290000000000 = 210 · 38 · 510 · 89	Discriminant
Eigenvalues	2+ 3+ 5+ -2  4 -2 -6  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-202976,35072976]	[a1,a2,a3,a4,a6]
Generators	[308:1296:1]	Generators of the group modulo torsion
j	903150162226196356/5702431640625	j-invariant
L	3.6026064524853	L(r)(E,1)/r!
Ω	0.42859427839424	Real period
R	2.1014083913945	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	10680b1 85440bp1 64080l1 106800l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21360a1

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

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Quadratic twists for elliptic curve 21360a1

-4	8	-3	5
10680b1	85440bp1	64080l1	106800l1

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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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