Cremona's table of elliptic curves

2852 = 2² · 23 · 31

Field	Data	Notes
Atkin-Lehner	2- 23+ 31-	Signs for the Atkin-Lehner involutions
Class	2852a	Isogeny class
Conductor	2852	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1080	Modular degree for the optimal curve
Δ	-182528 = -1 · 28 · 23 · 31	Discriminant
Eigenvalues	2-  1  0  5 -6 -4  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-828,8900]	[a1,a2,a3,a4,a6]
Generators	[12:2494:27]	Generators of the group modulo torsion
j	-245526946000/713	j-invariant
L	4.0060177275455	L(r)(E,1)/r!
Ω	2.784132076402	Real period
R	4.3166246617753	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	11408g1 45632b1 25668g1 71300g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2852a1

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	5	-6	-4	3	-4	+	-6	-	-10	3	-10	0	9	0	-7	11	0	-10	-10	-6	6	14

---

Quadratic twists for elliptic curve 2852a1

-4	8	-3	5	-23	-31
11408g1	45632b1	25668g1	71300g1	65596b1	88412f1

---

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