Cremona's table of elliptic curves

107712 = 2⁶ · 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 11+ 17+	Signs for the Atkin-Lehner involutions
Class	107712dn	Isogeny class
Conductor	107712	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	13401096192 = 215 · 37 · 11 · 17	Discriminant
Eigenvalues	2- 3- -2  0 11+ -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-215436,-38488016]	[a1,a2,a3,a4,a6]
Generators	[632:8820:1]	Generators of the group modulo torsion
j	46291481457416/561	j-invariant
L	4.4414074215301	L(r)(E,1)/r!
Ω	0.22160011720732	Real period
R	5.0106104164515	Regulator
r	1	Rank of the group of rational points
S	3.9999999993395	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	107712ep4 53856m4 35904dc4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 107712dn4

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	+	-4	0	-2	4	-6	-2	12	8	-6	12	2	0	0	-10	0	16	-2	-14

---

Quadratic twists for elliptic curve 107712dn4

-4	8	-3
107712ep4	53856m4	35904dc4

---

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