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	8112k	Isogeny class
Conductor	8112	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-231686832 = -1 · 24 · 3 · 136	Discriminant
Eigenvalues	2+ 3-  2  0  4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,113,-532]	[a1,a2,a3,a4,a6]
j	2048/3	j-invariant
L	3.7403442104052	L(r)(E,1)/r!
Ω	0.9350860526013	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4056a1 32448ci1 24336i1 48a4	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112k1

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	4	+	2	-4	8	6	8	-6	6	-4	0	-2	4	-2	-4	8	-10	8	-4	6	-2

---

Quadratic twists for elliptic curve 8112k1

-4	8	-3	13
4056a1	32448ci1	24336i1	48a4

---

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