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	8112r	Isogeny class
Conductor	8112	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	219894898998528 = 28 · 34 · 139	Discriminant
Eigenvalues	2+ 3-  0  2  2 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-18308,-638676]	[a1,a2,a3,a4,a6]
Generators	[-38:60:1]	Generators of the group modulo torsion
j	250000/81	j-invariant
L	5.4912540178303	L(r)(E,1)/r!
Ω	0.42099851538127	Real period
R	3.2608511771456	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	4056e2 32448cs2 24336s2 8112s2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112r2

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

---

Quadratic twists for elliptic curve 8112r2

-4	8	-3	13
4056e2	32448cs2	24336s2	8112s2

---

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