Cremona's table of elliptic curves

1638 = 2 · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	1638k	Isogeny class
Conductor	1638	Conductor
∏ cp	34	Product of Tamagawa factors cp
deg	544	Modular degree for the optimal curve
Δ	-322043904 = -1 · 217 · 33 · 7 · 13	Discriminant
Eigenvalues	2- 3+ -1 7+ -5 13- -1 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,82,-835]	[a1,a2,a3,a4,a6]
Generators	[9:19:1]	Generators of the group modulo torsion
j	2284322013/11927552	j-invariant
L	3.7272985150077	L(r)(E,1)/r!
Ω	0.86233089973318	Real period
R	0.12712802816867	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	13104bm1 52416b1 1638a1 40950j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1638k1

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	+	-5	-	-1	-1	-5	-1	-6	7	-2	1	0	-6	-6	-7	-8	-10	9	2	-2	6	14

---

Quadratic twists for elliptic curve 1638k1

-4	8	-3	5	-7	13
13104bm1	52416b1	1638a1	40950j1	11466bl1	21294l1

---

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