Cremona's table of elliptic curves

817 = 19 · 43

Field	Data	Notes
Atkin-Lehner	19- 43-	Signs for the Atkin-Lehner involutions
Class	817b	Isogeny class
Conductor	817	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	1160	Modular degree for the optimal curve
Δ	-53070047923 = -1 · 192 · 435	Discriminant
Eigenvalues	0 -2 -2  4  3  1 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-16649,821406]	[a1,a2,a3,a4,a6]
Generators	[-2:924:1]	Generators of the group modulo torsion
j	-510404220761669632/53070047923	j-invariant
L	1.4907042069483	L(r)(E,1)/r!
Ω	1.0755524992062	Real period
R	0.138598925487	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	13072e1 52288b1 7353o1 20425b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 817b1

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
0	-2	-2	4	3	1	-3	-	-5	-4	1	-8	-1	-	-8	-3	4	-6	11	-4	-2	-12	-13	-8	13

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Quadratic twists for elliptic curve 817b1

-4	8	-3	5	-7	-11	-19	-43
13072e1	52288b1	7353o1	20425b1	40033b1	98857a1	15523b1	35131b1

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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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