Cremona's table of elliptic curves

22720 = 2⁶ · 5 · 71

Field	Data	Notes
Atkin-Lehner	2+ 5+ 71+	Signs for the Atkin-Lehner involutions
Class	22720b	Isogeny class
Conductor	22720	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2580992000 = 212 · 53 · 712	Discriminant
Eigenvalues	2+  2 5+  0  4  4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-761,7961]	[a1,a2,a3,a4,a6]
Generators	[1655:696:125]	Generators of the group modulo torsion
j	11914842304/630125	j-invariant
L	7.5412478196843	L(r)(E,1)/r!
Ω	1.4232219774773	Real period
R	5.2987151259788	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	22720h2 11360g1 113600k2	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 22720b2

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	-4	4	-8	-2	-8	10	6	-2	-12	-4	12	2	-4	+	-14	-12	-6	2	-8

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Quadratic twists for elliptic curve 22720b2

-4	8	5
22720h2	11360g1	113600k2

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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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