Cremona's table of elliptic curves

56800 = 2⁵ · 5² · 71

Field	Data	Notes
Atkin-Lehner	2- 5+ 71+	Signs for the Atkin-Lehner involutions
Class	56800k	Isogeny class
Conductor	56800	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	568000000 = 29 · 56 · 71	Discriminant
Eigenvalues	2-  1 5+ -3 -4 -5  8  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-208,88]	[a1,a2,a3,a4,a6]
Generators	[-6:34:1] [18:50:1]	Generators of the group modulo torsion
j	125000/71	j-invariant
L	10.209801302442	L(r)(E,1)/r!
Ω	1.4070463950491	Real period
R	1.8140484454469	Regulator
r	2	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	56800e1 113600g1 2272a1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 56800k1

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	+	-3	-4	-5	8	1	-7	4	-7	4	-12	-1	3	-2	-6	-2	-8	+	-7	0	-12	-11	8

---

Quadratic twists for elliptic curve 56800k1

-4	8	5
56800e1	113600g1	2272a1

---

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