Cremona's table of elliptic curves

21360 = 2⁴ · 3 · 5 · 89

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 89-	Signs for the Atkin-Lehner involutions
Class	21360p	Isogeny class
Conductor	21360	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-84306297487564800 = -1 · 213 · 38 · 52 · 894	Discriminant
Eigenvalues	2- 3- 5- -4 -4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-209600,39418548]	[a1,a2,a3,a4,a6]
Generators	[196:2430:1]	Generators of the group modulo torsion
j	-248622066042206401/20582592160050	j-invariant
L	5.5981658969336	L(r)(E,1)/r!
Ω	0.33428019255	Real period
R	2.0933658431229	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2670d4 85440bd3 64080u3 106800bj3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21360p3

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	2	2	-4	4	-6	4	2	2	4	0	-2	12	-6	4	8	-6	-8	-4	-	2

---

Quadratic twists for elliptic curve 21360p3

-4	8	-3	5
2670d4	85440bd3	64080u3	106800bj3

---

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