Cremona's table of elliptic curves

4592 = 2⁴ · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 7+ 41-	Signs for the Atkin-Lehner involutions
Class	4592h	Isogeny class
Conductor	4592	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	90320011264 = 217 · 75 · 41	Discriminant
Eigenvalues	2-  1  1 7+ -2  4  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2800,-56108]	[a1,a2,a3,a4,a6]
Generators	[-33:38:1]	Generators of the group modulo torsion
j	592915705201/22050784	j-invariant
L	4.4328216143409	L(r)(E,1)/r!
Ω	0.65779394988126	Real period
R	3.3694606153957	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	574j1 18368x1 41328bd1 114800ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4592h1

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	1	+	-2	4	3	0	-4	-5	-7	-2	-	1	2	-1	-10	-13	2	3	4	15	6	-15	-7

---

Quadratic twists for elliptic curve 4592h1

-4	8	-3	5	-7
574j1	18368x1	41328bd1	114800ca1	32144s1

---

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