Cremona's table of elliptic curves

127296 = 2⁶ · 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 17+	Signs for the Atkin-Lehner involutions
Class	127296ba	Isogeny class
Conductor	127296	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-194889163628150784 = -1 · 216 · 36 · 132 · 176	Discriminant
Eigenvalues	2+ 3-  2  2 -2 13- 17+  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,70836,19961840]	[a1,a2,a3,a4,a6]
Generators	[-172:1640:1]	Generators of the group modulo torsion
j	822769797308/4079249161	j-invariant
L	9.7882895996355	L(r)(E,1)/r!
Ω	0.22878144154316	Real period
R	5.3480570118339	Regulator
r	1	Rank of the group of rational points
S	1.0000000059925	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	127296cy2 15912c2 14144n2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 127296ba2

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	2	-2	-	+	8	2	6	-10	-2	10	-8	0	6	0	-6	12	2	-2	6	-16	10	-10

---

Quadratic twists for elliptic curve 127296ba2

-4	8	-3
127296cy2	15912c2	14144n2

---

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