Cremona's table of elliptic curves

17040 = 2⁴ · 3 · 5 · 71

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 71-	Signs for the Atkin-Lehner involutions
Class	17040bb	Isogeny class
Conductor	17040	Conductor
∏ cp	224	Product of Tamagawa factors cp
deg	193536	Modular degree for the optimal curve
Δ	-55638556508160000 = -1 · 218 · 314 · 54 · 71	Discriminant
Eigenvalues	2- 3- 5- -2  6  4 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-78520,14134100]	[a1,a2,a3,a4,a6]
Generators	[140:2430:1]	Generators of the group modulo torsion
j	-13071040729863481/13583631960000	j-invariant
L	6.5258788511739	L(r)(E,1)/r!
Ω	0.3213000573656	Real period
R	0.36269383787012	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2130c1 68160cc1 51120y1 85200cd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040bb1

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
-	-	-	-2	6	4	-8	-4	-4	2	-6	2	0	4	-8	10	-10	-12	-8	-	-6	8	0	-2	10

---

Quadratic twists for elliptic curve 17040bb1

-4	8	-3	5
2130c1	68160cc1	51120y1	85200cd1

---

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