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	13104d	Isogeny class
Conductor	13104	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-23225516391168 = -1 · 28 · 33 · 76 · 134	Discriminant
Eigenvalues	2+ 3+ -2 7+ -2 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-57951,5374574]	[a1,a2,a3,a4,a6]
Generators	[65:1372:1]	Generators of the group modulo torsion
j	-3113886554501616/3360173089	j-invariant
L	3.6501000072137	L(r)(E,1)/r!
Ω	0.67285139146023	Real period
R	1.3562058626691	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	6552c2 52416dy2 13104c2 91728g2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104d2

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	+	-2	+	6	-4	-2	0	4	2	-2	4	0	12	0	6	12	-2	-2	0	-4	-2	-10

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Quadratic twists for elliptic curve 13104d2

-4	8	-3	-7
6552c2	52416dy2	13104c2	91728g2

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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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