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	16	Product of Tamagawa factors cp
Δ	198754238214350 = 2 · 52 · 77 · 136	Discriminant
Eigenvalues	2+  2 5- 7-  0 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-14872,-171366]	[a1,a2,a3,a4,a6]
Generators	[-15:228:1]	Generators of the group modulo torsion
j	3092354182009/1689383150	j-invariant
L	4.3758493679779	L(r)(E,1)/r!
Ω	0.46164592116659	Real period
R	2.369700005645	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	50960bt2 57330do2 31850cb2 910c2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370h2

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 6370h2

-4	-3	5	-7	13
50960bt2	57330do2	31850cb2	910c2	82810ca2

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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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