Cremona's table of elliptic curves

8112 = 2⁴ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3+ 13-	Signs for the Atkin-Lehner involutions
Class	8112w	Isogeny class
Conductor	8112	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	400306447243542528 = 222 · 32 · 139	Discriminant
Eigenvalues	2- 3+  2 -2  0 13-  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-191974592,-1023732753408]	[a1,a2,a3,a4,a6]
Generators	[-9231803068939935968:-21006182189288960:1154089580209957]	Generators of the group modulo torsion
j	18013780041269221/9216	j-invariant
L	3.9584029325211	L(r)(E,1)/r!
Ω	0.040559128641142	Real period
R	24.398964333925	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	1014g4 32448dm4 24336ce4 8112y4	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112w4

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

---

Quadratic twists for elliptic curve 8112w4

-4	8	-3	13
1014g4	32448dm4	24336ce4	8112y4

---

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