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	21840bz	Isogeny class
Conductor	21840	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	67629219840 = 218 · 34 · 5 · 72 · 13	Discriminant
Eigenvalues	2- 3- 5+ 7-  2 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1456,-17836]	[a1,a2,a3,a4,a6]
Generators	[-28:42:1]	Generators of the group modulo torsion
j	83396175409/16511040	j-invariant
L	6.385736848968	L(r)(E,1)/r!
Ω	0.78351621433071	Real period
R	1.0187627154632	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	2730s1 87360fj1 65520el1 109200cv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840bz1

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

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Quadratic twists for elliptic curve 21840bz1

-4	8	-3	5
2730s1	87360fj1	65520el1	109200cv1

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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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