Cremona's table of elliptic curves

338 = 2 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13-	Signs for the Atkin-Lehner involutions
Class	338d	Isogeny class
Conductor	338	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	-84835994984 = -1 · 23 · 139	Discriminant
Eigenvalues	2+ -1  3  3  0 13- -3  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,504,-13112]	[a1,a2,a3,a4,a6]
j	1331/8	j-invariant
L	1.0792546782682	L(r)(E,1)/r!
Ω	0.53962733913408	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2704m1 10816t1 3042o1 8450v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 338d1

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
+	-1	3	3	0	-	-3	6	6	0	0	3	0	1	3	-6	-6	-8	12	-15	6	10	-6	-6	12

---

Quadratic twists for elliptic curve 338d1

-4	8	-3	5	-7	-11	13	17	-19
2704m1	10816t1	3042o1	8450v1	16562v1	40898ca1	338e1	97682j1	122018bi1

---

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