Cremona's table of elliptic curves

690 = 2 · 3 · 5 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 23+	Signs for the Atkin-Lehner involutions
Class	690k	Isogeny class
Conductor	690	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	293666194803750 = 2 · 3 · 54 · 238	Discriminant
Eigenvalues	2- 3- 5-  0  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-25830,-1370850]	[a1,a2,a3,a4,a6]
j	1905890658841300321/293666194803750	j-invariant
L	3.0439311062815	L(r)(E,1)/r!
Ω	0.38049138828518	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	5520u5 22080d6 2070f5 3450d5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690k5

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	4	-2	-6	4	+	-2	0	-2	10	-4	0	6	-4	-10	-12	-8	10	-8	-4	18	2

---

Quadratic twists for elliptic curve 690k5

-4	8	-3	5	-7	-11	13	-23
5520u5	22080d6	2070f5	3450d5	33810ca6	83490bb6	116610y6	15870bg5

---

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