Cremona's table of elliptic curves

4592 = 2⁴ · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 7- 41+	Signs for the Atkin-Lehner involutions
Class	4592b	Isogeny class
Conductor	4592	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	28801024 = 211 · 73 · 41	Discriminant
Eigenvalues	2+ -1 -3 7- -6  0 -7  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-112,416]	[a1,a2,a3,a4,a6]
Generators	[-11:14:1] [-4:28:1]	Generators of the group modulo torsion
j	76545506/14063	j-invariant
L	3.5751265262647	L(r)(E,1)/r!
Ω	1.9961999697696	Real period
R	0.14924717715355	Regulator
r	2	Rank of the group of rational points
S	0.99999999999982	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2296a1 18368y1 41328m1 114800c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4592b1

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	-	-6	0	-7	0	-8	-3	-7	2	+	-3	-10	9	6	-1	2	-15	-8	-11	-6	3	3

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Quadratic twists for elliptic curve 4592b1

-4	8	-3	5	-7
2296a1	18368y1	41328m1	114800c1	32144g1

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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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