Cremona's table of elliptic curves

8096 = 2⁵ · 11 · 23

Field	Data	Notes
Atkin-Lehner	2+ 11+ 23+	Signs for the Atkin-Lehner involutions
Class	8096a	Isogeny class
Conductor	8096	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	103488	Modular degree for the optimal curve
Δ	1777350193317906944 = 29 · 1111 · 233	Discriminant
Eigenvalues	2+  2  1 -1 11+ -5  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-375640,-61016856]	[a1,a2,a3,a4,a6]
Generators	[-750263020741545465:11147400331806285516:3438506718650375]	Generators of the group modulo torsion
j	11449075068218623688/3471387096324037	j-invariant
L	5.9499603151747	L(r)(E,1)/r!
Ω	0.19738141787654	Real period
R	30.144480565523	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8096b1 16192z1 72864bi1 89056k1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8096a1

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	1	-1	+	-5	3	2	+	7	1	3	-10	-12	7	-6	-10	0	7	-5	8	-5	4	-10	2

---

Quadratic twists for elliptic curve 8096a1

-4	8	-3	-11
8096b1	16192z1	72864bi1	89056k1

---

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