Cremona's table of elliptic curves

5313 = 3 · 7 · 11 · 23

Field	Data	Notes
Atkin-Lehner	3- 7+ 11- 23-	Signs for the Atkin-Lehner involutions
Class	5313d	Isogeny class
Conductor	5313	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	-3099832659 = -1 · 36 · 75 · 11 · 23	Discriminant
Eigenvalues	2 3- -1 7+ 11-  6 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,364,-103]	[a1,a2,a3,a4,a6]
j	5319051554816/3099832659	j-invariant
L	5.0361233916436	L(r)(E,1)/r!
Ω	0.83935389860726	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	85008bs1 15939d1 37191d1 58443r1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 5313d1

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	-	-1	+	-	6	-2	2	-	6	10	-8	7	5	4	6	6	-10	4	3	13	7	-16	3	18

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Quadratic twists for elliptic curve 5313d1

-4	-3	-7	-11	-23
85008bs1	15939d1	37191d1	58443r1	122199k1

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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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