Cremona's table of elliptic curves

1394 = 2 · 17 · 41

Field	Data	Notes
Atkin-Lehner	2+ 17+ 41+	Signs for the Atkin-Lehner involutions
Class	1394b	Isogeny class
Conductor	1394	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	12133376 = 210 · 172 · 41	Discriminant
Eigenvalues	2+  0  2 -2  0  0 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-236,-1328]	[a1,a2,a3,a4,a6]
Generators	[-9:7:1]	Generators of the group modulo torsion
j	1457117049753/12133376	j-invariant
L	2.1343757775001	L(r)(E,1)/r!
Ω	1.2184380748093	Real period
R	1.7517310248485	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	11152l1 44608c1 12546q1 34850u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1394b1

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	0	0	+	4	0	-8	-8	-2	+	-4	6	0	-4	14	-4	-14	6	-10	-12	18	-10

---

Quadratic twists for elliptic curve 1394b1

-4	8	-3	5	-7	17	41
11152l1	44608c1	12546q1	34850u1	68306l1	23698c1	57154e1

---

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