Cremona's table of elliptic curves

13104 = 2⁴ · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	13104o	Isogeny class
Conductor	13104	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	895468234752 = 211 · 37 · 7 · 134	Discriminant
Eigenvalues	2+ 3- -2 7+ -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8571,-302006]	[a1,a2,a3,a4,a6]
Generators	[-54:58:1] [-49:18:1]	Generators of the group modulo torsion
j	46640233586/599781	j-invariant
L	5.797226347778	L(r)(E,1)/r!
Ω	0.49656892390095	Real period
R	5.8372826698809	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6552v3 52416fi4 4368f3 91728bo4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104o3

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	+	-4	+	-2	-4	-4	-10	-8	2	-10	-4	-8	6	-8	2	8	8	6	-8	8	-2	14

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Quadratic twists for elliptic curve 13104o3

-4	8	-3	-7
6552v3	52416fi4	4368f3	91728bo4

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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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