Cremona's table of elliptic curves

408 = 2³ · 3 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 17-	Signs for the Atkin-Lehner involutions
Class	408b	Isogeny class
Conductor	408	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1539459072 = -1 · 211 · 32 · 174	Discriminant
Eigenvalues	2- 3-  2 -4  4  6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,288,288]	[a1,a2,a3,a4,a6]
j	1285471294/751689	j-invariant
L	1.8237015160132	L(r)(E,1)/r!
Ω	0.91185075800658	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	816b4 3264i4 1224c4 10200c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 408b4

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
-	-	2	-4	4	6	-	4	-4	-6	-4	10	-6	4	-8	6	-4	-14	-12	-12	10	-4	4	-6	-6

---

Quadratic twists for elliptic curve 408b4

-4	8	-3	5	-7	-11	13	17
816b4	3264i4	1224c4	10200c4	19992v4	49368n3	68952o3	6936h4

---

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