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	21840f	Isogeny class
Conductor	21840	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	19192992000 = 28 · 3 · 53 · 7 · 134	Discriminant
Eigenvalues	2+ 3+ 5- 7+ -4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1100,-12000]	[a1,a2,a3,a4,a6]
Generators	[-20:40:1] [-15:30:1]	Generators of the group modulo torsion
j	575514878416/74972625	j-invariant
L	6.700607740262	L(r)(E,1)/r!
Ω	0.83605288340237	Real period
R	2.671524681945	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10920i1 87360fz1 65520o1 109200cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840f1

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

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Quadratic twists for elliptic curve 21840f1

-4	8	-3	5
10920i1	87360fz1	65520o1	109200cb1

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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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