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	21840by	Isogeny class
Conductor	21840	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	19416983040000 = 212 · 35 · 54 · 74 · 13	Discriminant
Eigenvalues	2- 3- 5+ 7-  0 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-269976,-54082476]	[a1,a2,a3,a4,a6]
Generators	[-300:18:1]	Generators of the group modulo torsion
j	531301262949272089/4740474375	j-invariant
L	6.4647496122824	L(r)(E,1)/r!
Ω	0.2094442121854	Real period
R	1.5433106374312	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	1365a3 87360fi4 65520ek4 109200ct4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840by4

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

---

Quadratic twists for elliptic curve 21840by4

-4	8	-3	5
1365a3	87360fi4	65520ek4	109200ct4

---

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