Cremona's table of elliptic curves

705 = 3 · 5 · 47

Field	Data	Notes
Atkin-Lehner	3- 5- 47-	Signs for the Atkin-Lehner involutions
Class	705f	Isogeny class
Conductor	705	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	310640625 = 32 · 56 · 472	Discriminant
Eigenvalues	1 3- 5-  0  4  2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-373,2603]	[a1,a2,a3,a4,a6]
j	5717095008841/310640625	j-invariant
L	2.5454221899006	L(r)(E,1)/r!
Ω	1.6969481266004	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	11280o2 45120d2 2115e2 3525b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 705f2

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	4	2	6	0	0	-2	4	-2	-6	-4	-	-6	0	-2	-4	4	-2	0	-4	-14	10

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Quadratic twists for elliptic curve 705f2

-4	8	-3	5	-7	-11	13	-47
11280o2	45120d2	2115e2	3525b2	34545b2	85305bd2	119145e2	33135h2

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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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