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	5313b	Isogeny class
Conductor	5313	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2176	Modular degree for the optimal curve
Δ	-36293103 = -1 · 34 · 7 · 112 · 232	Discriminant
Eigenvalues	1 3+ -4 7- 11- -4 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-72,-405]	[a1,a2,a3,a4,a6]
Generators	[54:369:1]	Generators of the group modulo torsion
j	-42180533641/36293103	j-invariant
L	2.831788199454	L(r)(E,1)/r!
Ω	0.78946417453891	Real period
R	1.7934874632582	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	85008ca1 15939h1 37191f1 58443d1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 5313b1

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	+	-4	-	-	-4	-2	8	+	2	4	2	8	4	-12	-10	0	-2	8	-8	-8	8	12	0	-8

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Quadratic twists for elliptic curve 5313b1

-4	-3	-7	-11	-23
85008ca1	15939h1	37191f1	58443d1	122199a1

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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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