Cremona's table of elliptic curves

2736 = 2⁴ · 3² · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 19-	Signs for the Atkin-Lehner involutions
Class	2736u	Isogeny class
Conductor	2736	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-113689008 = -1 · 24 · 39 · 192	Discriminant
Eigenvalues	2- 3- -2  0  2  2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,24,511]	[a1,a2,a3,a4,a6]
j	131072/9747	j-invariant
L	1.4297432565747	L(r)(E,1)/r!
Ω	1.4297432565747	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	684b1 10944by1 912j1 68400ez1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2736u1

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
-	-	-2	0	2	2	-6	-	2	-4	8	-2	8	8	2	4	0	2	-12	-4	6	16	6	0	-2

---

Quadratic twists for elliptic curve 2736u1

-4	8	-3	5	-19
684b1	10944by1	912j1	68400ez1	51984cs1

---

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