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	12	Product of Tamagawa factors cp
Δ	34423828125 = 3 · 512 · 47	Discriminant
Eigenvalues	1 3- 5-  0  4  2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1078,-10369]	[a1,a2,a3,a4,a6]
j	138356873478361/34423828125	j-invariant
L	2.5454221899006	L(r)(E,1)/r!
Ω	0.84847406330021	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	11280o3 45120d4 2115e3 3525b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 705f3

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 705f3

-4	8	-3	5	-7	-11	13	-47
11280o3	45120d4	2115e3	3525b3	34545b4	85305bd4	119145e4	33135h4

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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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