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	8	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	253305355940 = 22 · 5 · 78 · 133	Discriminant
Eigenvalues	2+  2 5- 7-  0 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-11442,-475264]	[a1,a2,a3,a4,a6]
Generators	[1070:34304:1]	Generators of the group modulo torsion
j	1408317602329/2153060	j-invariant
L	4.3758493679779	L(r)(E,1)/r!
Ω	0.46164592116659	Real period
R	4.7394000112901	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	50960bt1 57330do1 31850cb1 910c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370h1

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 6370h1

-4	-3	5	-7	13
50960bt1	57330do1	31850cb1	910c1	82810ca1

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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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