Cremona's table of elliptic curves

782 = 2 · 17 · 23

Field	Data	Notes
Atkin-Lehner	2- 17+ 23+	Signs for the Atkin-Lehner involutions
Class	782b	Isogeny class
Conductor	782	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	-3128 = -1 · 23 · 17 · 23	Discriminant
Eigenvalues	2-  1 -4  3  6  6 17+ -3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-60,-184]	[a1,a2,a3,a4,a6]
j	-23912763841/3128	j-invariant
L	2.5728347933043	L(r)(E,1)/r!
Ω	0.8576115977681	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	6256d1 25024a1 7038i1 19550l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 782b1

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	-4	3	6	6	+	-3	+	2	4	-2	4	8	1	1	-8	-2	-11	-6	10	-11	-12	-10	-17

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Quadratic twists for elliptic curve 782b1

-4	8	-3	5	-7	-11	17	-23
6256d1	25024a1	7038i1	19550l1	38318s1	94622f1	13294h1	17986i1

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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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