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	13104br	Isogeny class
Conductor	13104	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	-111424045824 = -1 · 28 · 314 · 7 · 13	Discriminant
Eigenvalues	2- 3- -1 7+ -6 13+  8 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3288,-74324]	[a1,a2,a3,a4,a6]
Generators	[98:738:1]	Generators of the group modulo torsion
j	-21064523776/597051	j-invariant
L	3.8841737864803	L(r)(E,1)/r!
Ω	0.31471028445058	Real period
R	3.0855154553189	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	3276i1 52416fd1 4368u1 91728fi1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104br1

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	+	-6	+	8	-3	9	9	1	-8	-2	-9	-3	5	8	-10	10	-12	3	7	-15	5	15

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Quadratic twists for elliptic curve 13104br1

-4	8	-3	-7
3276i1	52416fd1	4368u1	91728fi1

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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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