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	13104bt	Isogeny class
Conductor	13104	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	559209111552 = 213 · 37 · 74 · 13	Discriminant
Eigenvalues	2- 3- -2 7+ -4 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-60051,5663954]	[a1,a2,a3,a4,a6]
Generators	[145:72:1]	Generators of the group modulo torsion
j	8020417344913/187278	j-invariant
L	3.4066572228306	L(r)(E,1)/r!
Ω	0.85295744428473	Real period
R	0.49924196770558	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	1638i3 52416fj4 4368o3 91728fo4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104bt3

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	+	-6	4	0	6	8	10	6	-4	4	-10	4	-6	8	0	-10	8	4	6	-2

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Quadratic twists for elliptic curve 13104bt3

-4	8	-3	-7
1638i3	52416fj4	4368o3	91728fo4

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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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