Cremona's table of elliptic curves

58800 = 2⁴ · 3 · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7+	Signs for the Atkin-Lehner involutions
Class	58800gm	Isogeny class
Conductor	58800	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	276595200000000 = 215 · 32 · 58 · 74	Discriminant
Eigenvalues	2- 3+ 5- 7+  0 -4  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4469208,3638076912]	[a1,a2,a3,a4,a6]
Generators	[1218:174:1]	Generators of the group modulo torsion
j	2569823930905/72	j-invariant
L	4.5171659760926	L(r)(E,1)/r!
Ω	0.40154664628077	Real period
R	2.8123544412622	Regulator
r	1	Rank of the group of rational points
S	0.9999999999836	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7350be2 58800hr2 58800jo2	Quadratic twists by: -4 5 -7

Hecke Eigenvalues for elliptic curve 58800gm2

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
-	+	-	+	0	-4	3	-2	-3	0	1	-10	-9	10	3	-6	6	8	4	-3	14	-11	0	-15	-7

---

Quadratic twists for elliptic curve 58800gm2

-4	5	-7
7350be2	58800hr2	58800jo2

---

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