Cremona's table of elliptic curves

12768 = 2⁵ · 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	12768z	Isogeny class
Conductor	12768	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	1201264131207168 = 212 · 38 · 73 · 194	Discriminant
Eigenvalues	2- 3-  2 7+  0 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40817,-2714337]	[a1,a2,a3,a4,a6]
j	1836105571609408/293277375783	j-invariant
L	2.7160623848927	L(r)(E,1)/r!
Ω	0.33950779811159	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12768n2 25536bs1 38304n3 89376bm3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12768z3

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	-6	-	0	-2	0	6	6	0	-8	6	4	2	4	12	2	-4	12	14	-10

---

Quadratic twists for elliptic curve 12768z3

-4	8	-3	-7
12768n2	25536bs1	38304n3	89376bm3

---

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