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	3	Product of Tamagawa factors cp
deg	108	Modular degree for the optimal curve
Δ	17625 = 3 · 53 · 47	Discriminant
Eigenvalues	1 3- 5-  0  4  2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-368,2681]	[a1,a2,a3,a4,a6]
j	5489965305721/17625	j-invariant
L	2.5454221899006	L(r)(E,1)/r!
Ω	3.3938962532008	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	11280o1 45120d1 2115e1 3525b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 705f1

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 705f1

-4	8	-3	5	-7	-11	13	-47
11280o1	45120d1	2115e1	3525b1	34545b1	85305bd1	119145e1	33135h1

---

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