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	48	Product of Tamagawa factors cp
Δ	-49406770125 = -1 · 34 · 53 · 474	Discriminant
Eigenvalues	1 3- 5-  0  4  2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,252,10603]	[a1,a2,a3,a4,a6]
j	1779919481159/49406770125	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	4	Number of elements in the torsion subgroup
Twists	11280o4 45120d3 2115e4 3525b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 705f4

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

---

Quadratic twists for elliptic curve 705f4

-4	8	-3	5	-7	-11	13	-47
11280o4	45120d3	2115e4	3525b4	34545b3	85305bd3	119145e3	33135h3

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations