Cremona's table of elliptic curves

22800 = 2⁴ · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 19+	Signs for the Atkin-Lehner involutions
Class	22800ct	Isogeny class
Conductor	22800	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	2166091405200 = 24 · 37 · 52 · 195	Discriminant
Eigenvalues	2- 3- 5+ -1  4  0 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10238,-395817]	[a1,a2,a3,a4,a6]
Generators	[-53:27:1]	Generators of the group modulo torsion
j	296723207944960/5415228513	j-invariant
L	6.4073106727765	L(r)(E,1)/r!
Ω	0.47514195984118	Real period
R	1.9264349888545	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	5700e1 91200fu1 68400ed1 22800ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22800ct1

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	4	0	-4	+	-6	-1	-4	8	5	4	6	-3	11	-13	-14	-15	13	2	14	-15	2

---

Quadratic twists for elliptic curve 22800ct1

-4	8	-3	5
5700e1	91200fu1	68400ed1	22800ck1

---

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