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	13104bq	Isogeny class
Conductor	13104	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-7869374847000576 = -1 · 213 · 37 · 7 · 137	Discriminant
Eigenvalues	2- 3-  1 7+  5 13+  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-529127427,-4684772695678]	[a1,a2,a3,a4,a6]
Generators	[444334767782959776334670399:422798519632605076518445368:16728392586532077449207]	Generators of the group modulo torsion
j	-5486773802537974663600129/2635437714	j-invariant
L	5.2944716334634	L(r)(E,1)/r!
Ω	0.015739085355848	Real period
R	42.048755643671	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1638h2 52416fg2 4368n2 91728fl2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104bq2

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	+	5	+	3	1	3	-9	-4	-11	0	5	-8	2	4	-15	2	-12	11	-10	-14	-6	-14

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Quadratic twists for elliptic curve 13104bq2

-4	8	-3	-7
1638h2	52416fg2	4368n2	91728fl2

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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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