Cremona's table of elliptic curves

2640 = 2⁴ · 3 · 5 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	2640f	Isogeny class
Conductor	2640	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	39600000000 = 210 · 32 · 58 · 11	Discriminant
Eigenvalues	2+ 3+ 5-  0 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2320,-41168]	[a1,a2,a3,a4,a6]
Generators	[-26:30:1]	Generators of the group modulo torsion
j	1349195526724/38671875	j-invariant
L	2.9680177178993	L(r)(E,1)/r!
Ω	0.68908497714956	Real period
R	0.53839835004397	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	1320m4 10560ca3 7920c4 13200u3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2640f3

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	2	-4	-8	-2	-8	6	2	4	0	6	-4	-10	12	0	2	-8	-12	-6	-14

---

Quadratic twists for elliptic curve 2640f3

-4	8	-3	5	-7	-11
1320m4	10560ca3	7920c4	13200u3	129360ca3	29040n3

---

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