Cremona's table of elliptic curves

21840 = 2⁴ · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7- 13+	Signs for the Atkin-Lehner involutions
Class	21840ci	Isogeny class
Conductor	21840	Conductor
∏ cp	120	Product of Tamagawa factors cp
deg	161280	Modular degree for the optimal curve
Δ	4726470916177920 = 226 · 35 · 5 · 73 · 132	Discriminant
Eigenvalues	2- 3- 5- 7-  2 13+ -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-130040,-17787180]	[a1,a2,a3,a4,a6]
Generators	[-212:546:1]	Generators of the group modulo torsion
j	59374229431741561/1153923563520	j-invariant
L	7.2799986614536	L(r)(E,1)/r!
Ω	0.25170555975595	Real period
R	0.96408924095176	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	2730g1 87360es1 65520cy1 109200df1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840ci1

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

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Quadratic twists for elliptic curve 21840ci1

-4	8	-3	5
2730g1	87360es1	65520cy1	109200df1

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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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