Cremona's table of elliptic curves

21840 = 2⁴ · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	21840l	Isogeny class
Conductor	21840	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	10032750000000000 = 210 · 32 · 512 · 73 · 13	Discriminant
Eigenvalues	2+ 3- 5+ 7+ -4 13+  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-861336,-307935036]	[a1,a2,a3,a4,a6]
j	69014771940559650916/9797607421875	j-invariant
L	1.2537185434099	L(r)(E,1)/r!
Ω	0.15671481792623	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10920c4 87360ff4 65520bd4 109200v4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840l4

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	+	6	-8	-4	-2	-4	10	6	-8	-8	-2	8	-2	4	-8	-10	16	-12	-18	-2

---

Quadratic twists for elliptic curve 21840l4

-4	8	-3	5
10920c4	87360ff4	65520bd4	109200v4

---

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