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	32	Product of Tamagawa factors cp
Δ	-23775897600 = -1 · 211 · 36 · 52 · 72 · 13	Discriminant
Eigenvalues	2+ 3+ 5- 7+  2 13-  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,240,7200]	[a1,a2,a3,a4,a6]
Generators	[12:108:1]	Generators of the group modulo torsion
j	743389918/11609325	j-invariant
L	4.8646681519929	L(r)(E,1)/r!
Ω	0.89106708560264	Real period
R	0.68242170407165	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	10920v2 87360fx2 65520r2 109200bw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840h2

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 21840h2

-4	8	-3	5
10920v2	87360fx2	65520r2	109200bw2

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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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