Cremona's table of elliptic curves

2604 = 2² · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 31-	Signs for the Atkin-Lehner involutions
Class	2604f	Isogeny class
Conductor	2604	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	70068432 = 24 · 3 · 72 · 313	Discriminant
Eigenvalues	2- 3-  0 7-  0 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-29793,-1989300]	[a1,a2,a3,a4,a6]
Generators	[5700:29260:27]	Generators of the group modulo torsion
j	182793612716032000/4379277	j-invariant
L	3.7961522695263	L(r)(E,1)/r!
Ω	0.3633873303689	Real period
R	6.9643819918408	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	10416o3 41664x3 7812j3 65100c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2604f3

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

---

Quadratic twists for elliptic curve 2604f3

-4	8	-3	5	-7	-31
10416o3	41664x3	7812j3	65100c3	18228a3	80724i3

---

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