Cremona's table of elliptic curves

22320 = 2⁴ · 3² · 5 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 31-	Signs for the Atkin-Lehner involutions
Class	22320k	Isogeny class
Conductor	22320	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	31023212958720 = 210 · 38 · 5 · 314	Discriminant
Eigenvalues	2+ 3- 5+ -4 -4 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11523,-393518]	[a1,a2,a3,a4,a6]
Generators	[-51:248:1]	Generators of the group modulo torsion
j	226669409284/41558445	j-invariant
L	3.1134382699853	L(r)(E,1)/r!
Ω	0.4666195357512	Real period
R	0.83404091327131	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11160m4 89280gc3 7440h4 111600bs3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 22320k3

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
+	-	+	-4	-4	-6	2	4	0	-6	-	10	-10	-4	12	6	12	-2	0	8	-2	8	-4	-10	10

---

Quadratic twists for elliptic curve 22320k3

-4	8	-3	5
11160m4	89280gc3	7440h4	111600bs3

---

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