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	705c	Isogeny class
Conductor	705	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-116800875 = -1 · 32 · 53 · 473	Discriminant
Eigenvalues	0 3- 5+  2 -6  5  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-81,-619]	[a1,a2,a3,a4,a6]
j	-59501707264/116800875	j-invariant
L	1.4948245968608	L(r)(E,1)/r!
Ω	0.74741229843038	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11280m2 45120j2 2115k2 3525f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 705c2

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	-6	5	6	2	9	-6	2	-4	0	11	+	6	9	-1	-4	-15	11	11	0	-3	2

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Quadratic twists for elliptic curve 705c2

-4	8	-3	5	-7	-11	13	-47
11280m2	45120j2	2115k2	3525f2	34545p2	85305n2	119145p2	33135j2

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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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