Cremona's table of elliptic curves

22704 = 2⁴ · 3 · 11 · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+ 43-	Signs for the Atkin-Lehner involutions
Class	22704v	Isogeny class
Conductor	22704	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-53565456384 = -1 · 222 · 33 · 11 · 43	Discriminant
Eigenvalues	2- 3+ -1  3 11+  4  3  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-936,15984]	[a1,a2,a3,a4,a6]
Generators	[68:512:1]	Generators of the group modulo torsion
j	-22164361129/13077504	j-invariant
L	5.0650556684768	L(r)(E,1)/r!
Ω	1.0386330019957	Real period
R	1.2191639536642	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	2838c1 90816cn1 68112cg1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 22704v1

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	+	4	3	4	6	2	-3	-10	1	-	2	0	-14	-5	-13	1	-9	-4	-1	-5	-13

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Quadratic twists for elliptic curve 22704v1

-4	8	-3
2838c1	90816cn1	68112cg1

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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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