Cremona's table of elliptic curves

2397 = 3 · 17 · 47

Field	Data	Notes
Atkin-Lehner	3- 17- 47+	Signs for the Atkin-Lehner involutions
Class	2397d	Isogeny class
Conductor	2397	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	1408	Modular degree for the optimal curve
Δ	2406187701 = 311 · 172 · 47	Discriminant
Eigenvalues	0 3- -1  3  1 -6 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1751,27527]	[a1,a2,a3,a4,a6]
Generators	[-17:229:1]	Generators of the group modulo torsion
j	594059784454144/2406187701	j-invariant
L	3.162263666555	L(r)(E,1)/r!
Ω	1.4584230029347	Real period
R	0.098558002226684	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	38352l1 7191e1 59925b1 117453e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2397d1

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	3	1	-6	-	-2	-9	3	-2	11	-2	0	+	-4	4	-6	-10	0	-10	-5	2	12	-9

---

Quadratic twists for elliptic curve 2397d1

-4	-3	5	-7	17	-47
38352l1	7191e1	59925b1	117453e1	40749a1	112659k1

---

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