Cremona's table of elliptic curves

5642 = 2 · 7 · 13 · 31

Field	Data	Notes
Atkin-Lehner	2+ 7- 13+ 31-	Signs for the Atkin-Lehner involutions
Class	5642f	Isogeny class
Conductor	5642	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1120	Modular degree for the optimal curve
Δ	-1173536 = -1 · 25 · 7 · 132 · 31	Discriminant
Eigenvalues	2+  1  1 7- -2 13+ -6  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-183,-966]	[a1,a2,a3,a4,a6]
Generators	[48:294:1]	Generators of the group modulo torsion
j	-672451615081/1173536	j-invariant
L	3.5596590018163	L(r)(E,1)/r!
Ω	0.6493756858837	Real period
R	2.7408317551743	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	45136d1 50778bn1 39494h1 73346n1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 5642f1

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	1	-	-2	+	-6	6	5	-1	-	-2	2	2	1	-2	12	-14	-7	10	1	-5	5	-11	-18

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Quadratic twists for elliptic curve 5642f1

-4	-3	-7	13
45136d1	50778bn1	39494h1	73346n1

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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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