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	782c	Isogeny class
Conductor	782	Conductor
∏ cp	28	Product of Tamagawa factors cp
Δ	2896879967514752 = 27 · 172 · 238	Discriminant
Eigenvalues	2- -2  0  4 -2  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-99793,-11862615]	[a1,a2,a3,a4,a6]
j	109906713160213524625/2896879967514752	j-invariant
L	1.8833070233319	L(r)(E,1)/r!
Ω	0.26904386047598	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6256e2 25024b2 7038f2 19550o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 782c2

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	0	4	-2	2	+	4	+	8	4	12	6	0	0	-14	0	-4	16	-8	-14	16	8	-6	-18

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Quadratic twists for elliptic curve 782c2

-4	8	-3	5	-7	-11	17	-23
6256e2	25024b2	7038f2	19550o2	38318t2	94622g2	13294i2	17986k2

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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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