Cremona's table of elliptic curves

3648 = 2⁶ · 3 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 19-	Signs for the Atkin-Lehner involutions
Class	3648i	Isogeny class
Conductor	3648	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1323483660288 = -1 · 217 · 312 · 19	Discriminant
Eigenvalues	2+ 3+ -2  0  0 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2271,-37215]	[a1,a2,a3,a4,a6]
j	9878111854/10097379	j-invariant
L	0.93174759737454	L(r)(E,1)/r!
Ω	0.46587379868727	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	3648bg4 456b4 10944be4 91200dm3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3648i4

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

---

Quadratic twists for elliptic curve 3648i4

-4	8	-3	5	-19
3648bg4	456b4	10944be4	91200dm3	69312bt3

---

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