Cremona's table of elliptic curves

1617 = 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	3- 7- 11-	Signs for the Atkin-Lehner involutions
Class	1617j	Isogeny class
Conductor	1617	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	34941753 = 33 · 76 · 11	Discriminant
Eigenvalues	1 3-  2 7- 11-  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-320,2153]	[a1,a2,a3,a4,a6]
j	30664297/297	j-invariant
L	3.1121217016744	L(r)(E,1)/r!
Ω	2.0747478011163	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	25872bk1 103488bb1 4851j1 40425y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1617j1

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	-	2	-	-	2	2	0	8	-6	8	6	2	0	-8	6	4	-6	-4	0	14	-4	-12	6	-2

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Quadratic twists for elliptic curve 1617j1

-4	8	-3	5	-7	-11
25872bk1	103488bb1	4851j1	40425y1	33a2	17787u1

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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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