Cremona's table of elliptic curves

22736 = 2⁴ · 7² · 29

Field	Data	Notes
Atkin-Lehner	2- 7+ 29-	Signs for the Atkin-Lehner involutions
Class	22736r	Isogeny class
Conductor	22736	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	32307856 = 24 · 74 · 292	Discriminant
Eigenvalues	2-  1  3 7+  1  2 -7 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-114,-421]	[a1,a2,a3,a4,a6]
Generators	[-5:7:1]	Generators of the group modulo torsion
j	4302592/841	j-invariant
L	7.5557997986649	L(r)(E,1)/r!
Ω	1.4798967236231	Real period
R	0.85093773527732	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5684b1 90944cp1 22736bm1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 22736r1

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
-	1	3	+	1	2	-7	-5	5	-	1	9	-6	12	-9	-9	3	-15	-5	-16	-3	7	-12	1	-14

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Quadratic twists for elliptic curve 22736r1

-4	8	-7
5684b1	90944cp1	22736bm1

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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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