Cremona's table of elliptic curves

6370 = 2 · 5 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 5- 7- 13+	Signs for the Atkin-Lehner involutions
Class	6370h	Isogeny class
Conductor	6370	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	852469947875000 = 23 · 56 · 79 · 132	Discriminant
Eigenvalues	2+  2 5- 7-  0 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-718757,234238901]	[a1,a2,a3,a4,a6]
Generators	[97:12814:1]	Generators of the group modulo torsion
j	349046010201856969/7245875000	j-invariant
L	4.3758493679779	L(r)(E,1)/r!
Ω	0.46164592116659	Real period
R	0.78990000188168	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	50960bt4 57330do4 31850cb4 910c4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370h4

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	-6	6	-8	-10	12	-4	0	-12	-6	-2	-4	-6	10	-16	0	12	-2

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Quadratic twists for elliptic curve 6370h4

-4	-3	5	-7	13
50960bt4	57330do4	31850cb4	910c4	82810ca4

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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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