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	6270a	Isogeny class
Conductor	6270	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	1863016887600 = 24 · 32 · 52 · 11 · 196	Discriminant
Eigenvalues	2+ 3+ 5+  0 11-  2  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-7733,250173]	[a1,a2,a3,a4,a6]
Generators	[38:95:1]	Generators of the group modulo torsion
j	51151160533082329/1863016887600	j-invariant
L	2.4193107786684	L(r)(E,1)/r!
Ω	0.82771695723029	Real period
R	0.24357267275317	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	50160br2 18810bb2 31350cf2 68970bk2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6270a2

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	-	2	4	-	-2	-4	-10	-2	0	-4	2	2	10	-6	0	6	-16	0	16	6	-2

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Quadratic twists for elliptic curve 6270a2

-4	-3	5	-11	-19
50160br2	18810bb2	31350cf2	68970bk2	119130bp2

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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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