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	2736a	Isogeny class
Conductor	2736	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-9980928 = -1 · 210 · 33 · 192	Discriminant
Eigenvalues	2+ 3+  0  0  2 -2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,45,98]	[a1,a2,a3,a4,a6]
Generators	[1:12:1]	Generators of the group modulo torsion
j	364500/361	j-invariant
L	3.3054549234963	L(r)(E,1)/r!
Ω	1.5092075164988	Real period
R	0.54754811504726	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	1368e2 10944br2 2736b2 68400a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2736a2

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	2	-2	-4	+	2	-6	-4	2	2	-4	10	-6	4	2	-4	4	-6	-8	-2	-6	-10

---

Quadratic twists for elliptic curve 2736a2

-4	8	-3	5	-19
1368e2	10944br2	2736b2	68400a2	51984c2

---

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