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	21840h	Isogeny class
Conductor	21840	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	163537920 = 210 · 33 · 5 · 7 · 132	Discriminant
Eigenvalues	2+ 3+ 5- 7+  2 13-  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-280,1792]	[a1,a2,a3,a4,a6]
Generators	[-18:26:1]	Generators of the group modulo torsion
j	2379293284/159705	j-invariant
L	4.8646681519929	L(r)(E,1)/r!
Ω	1.7821341712053	Real period
R	1.3648434081433	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	10920v1 87360fx1 65520r1 109200bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840h1

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

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Quadratic twists for elliptic curve 21840h1

-4	8	-3	5
10920v1	87360fx1	65520r1	109200bw1

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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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