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	21840cg	Isogeny class
Conductor	21840	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	38293167144960000 = 224 · 32 · 54 · 74 · 132	Discriminant
Eigenvalues	2- 3- 5- 7+  4 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-333600,-73674252]	[a1,a2,a3,a4,a6]
Generators	[731:8580:1]	Generators of the group modulo torsion
j	1002404925316922401/9348917760000	j-invariant
L	7.124386372253	L(r)(E,1)/r!
Ω	0.19876385436701	Real period
R	4.480433826199	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2730x2 87360ec2 65520cv2 109200ds2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840cg2

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

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Quadratic twists for elliptic curve 21840cg2

-4	8	-3	5
2730x2	87360ec2	65520cv2	109200ds2

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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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