Cremona's table of elliptic curves

6270 = 2 · 3 · 5 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 11+ 19-	Signs for the Atkin-Lehner involutions
Class	6270g	Isogeny class
Conductor	6270	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	180184125000 = 23 · 3 · 56 · 113 · 192	Discriminant
Eigenvalues	2+ 3- 5+  2 11+  2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-170319,-27068774]	[a1,a2,a3,a4,a6]
Generators	[163587130:86718983:343000]	Generators of the group modulo torsion
j	546398303575251662569/180184125000	j-invariant
L	3.5415049278619	L(r)(E,1)/r!
Ω	0.23500878332254	Real period
R	15.069670493981	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50160bg4 18810bj4 31350bh4 68970cl4	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6270g4

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

---

Quadratic twists for elliptic curve 6270g4

-4	-3	5	-11	-19
50160bg4	18810bj4	31350bh4	68970cl4	119130x4

---

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