Cremona's table of elliptic curves

1708 = 2² · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 7- 61-	Signs for the Atkin-Lehner involutions
Class	1708a	Isogeny class
Conductor	1708	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	5356288 = 28 · 73 · 61	Discriminant
Eigenvalues	2-  1  0 7-  3  2  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-68,164]	[a1,a2,a3,a4,a6]
j	137842000/20923	j-invariant
L	2.3139018902985	L(r)(E,1)/r!
Ω	2.3139018902985	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	6832f1 27328f1 15372f1 42700d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1708a1

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	0	-	3	2	3	5	-3	6	-4	8	0	5	-9	12	12	-	5	9	-4	-7	9	-9	8

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Quadratic twists for elliptic curve 1708a1

-4	8	-3	5	-7	61
6832f1	27328f1	15372f1	42700d1	11956c1	104188a1

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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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