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	72	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-12100510620 = -1 · 22 · 36 · 5 · 112 · 193	Discriminant
Eigenvalues	2+ 3- 5+  2 11+  2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,516,-2714]	[a1,a2,a3,a4,a6]
Generators	[29:177:1]	Generators of the group modulo torsion
j	15236391945671/12100510620	j-invariant
L	3.5415049278619	L(r)(E,1)/r!
Ω	0.70502634996761	Real period
R	2.5116117489968	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	50160bg1 18810bj1 31350bh1 68970cl1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6270g1

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

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Quadratic twists for elliptic curve 6270g1

-4	-3	5	-11	-19
50160bg1	18810bj1	31350bh1	68970cl1	119130x1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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