Cremona's table of elliptic curves

492 = 2² · 3 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 41-	Signs for the Atkin-Lehner involutions
Class	492a	Isogeny class
Conductor	492	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-31488 = -1 · 28 · 3 · 41	Discriminant
Eigenvalues	2- 3+  0 -2 -1 -2 -1 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13,25]	[a1,a2,a3,a4,a6]
Generators	[3:-2:1]	Generators of the group modulo torsion
j	-1024000/123	j-invariant
L	1.6799595492551	L(r)(E,1)/r!
Ω	3.5983226104378	Real period
R	0.15562432195324	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	1968n1 7872m1 1476a1 12300k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 492a1

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	-1	-2	-1	-4	-6	5	-3	-3	-	-7	-3	10	0	1	2	3	-11	6	4	6	8

---

Quadratic twists for elliptic curve 492a1

-4	8	-3	5	-7	-11	13	41
1968n1	7872m1	1476a1	12300k1	24108e1	59532a1	83148a1	20172f1

---

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