Cremona's table of elliptic curves

338 = 2 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Class	338a	Isogeny class
Conductor	338	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-2768896 = -1 · 214 · 132	Discriminant
Eigenvalues	2+  0  1 -4 -4 13+  3  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-389,-2859]	[a1,a2,a3,a4,a6]
Generators	[26:51:1]	Generators of the group modulo torsion
j	-38575685889/16384	j-invariant
L	1.2776773619189	L(r)(E,1)/r!
Ω	0.5374261245969	Real period
R	1.1887004589489	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	2704d2 10816b2 3042l2 8450o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 338a2

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	1	-4	-4	+	3	0	-4	-1	-4	-3	9	-8	8	-9	4	7	-4	8	-11	-4	0	6	-2

---

Quadratic twists for elliptic curve 338a2

-4	8	-3	5	-7	-11	13	17	-19
2704d2	10816b2	3042l2	8450o2	16562d2	40898bg2	338b2	97682a2	122018bb2

---

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