Cremona's table of elliptic curves

2652 = 2² · 3 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 17+	Signs for the Atkin-Lehner involutions
Class	2652f	Isogeny class
Conductor	2652	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	43821648 = 24 · 36 · 13 · 172	Discriminant
Eigenvalues	2- 3-  0 -4  0 13- 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3153,67104]	[a1,a2,a3,a4,a6]
j	216727177216000/2738853	j-invariant
L	1.8440771648019	L(r)(E,1)/r!
Ω	1.8440771648019	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	10608r1 42432a1 7956g1 66300f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2652f1

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

---

Quadratic twists for elliptic curve 2652f1

-4	8	-3	5	-7	13	17
10608r1	42432a1	7956g1	66300f1	129948h1	34476k1	45084h1

---

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