Cremona's table of elliptic curves

104 = 2³ · 13

Field	Data	Notes
Atkin-Lehner	2- 13+	Signs for the Atkin-Lehner involutions
Class	104a	Isogeny class
Conductor	104	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-26624 = -1 · 211 · 13	Discriminant
Eigenvalues	2-  1 -1  5 -2 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16,-32]	[a1,a2,a3,a4,a6]
j	-235298/13	j-invariant
L	1.1836111472523	L(r)(E,1)/r!
Ω	1.1836111472523	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	208b1 832e1 936b1 2600c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 104a1

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	-1	5	-2	+	-3	-2	4	-6	-4	11	8	-1	9	-12	6	0	6	7	-2	12	-16	-10	-10

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Quadratic twists for elliptic curve 104a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
208b1	832e1	936b1	2600c1	5096j1	12584c1	1352a1	30056g1	37544f1	55016c1	87464a1	99944f1

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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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