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	5313c	Isogeny class
Conductor	5313	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1088	Modular degree for the optimal curve
Δ	-4032567 = -1 · 32 · 7 · 112 · 232	Discriminant
Eigenvalues	-1 3+  0 7- 11- -4  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-83,272]	[a1,a2,a3,a4,a6]
Generators	[0:16:1]	Generators of the group modulo torsion
j	-63282696625/4032567	j-invariant
L	2.1058636570429	L(r)(E,1)/r!
Ω	2.434394518161	Real period
R	0.43252308558304	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	85008by1 15939g1 37191g1 58443a1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 5313c1

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	+	0	-	-	-4	6	0	+	6	-4	-6	12	-12	-12	-6	0	14	4	0	16	0	-4	-12	-16

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Quadratic twists for elliptic curve 5313c1

-4	-3	-7	-11	-23
85008by1	15939g1	37191g1	58443a1	122199b1

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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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