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	6370o	Isogeny class
Conductor	6370	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	46592	Modular degree for the optimal curve
Δ	-409841321093750 = -1 · 2 · 58 · 79 · 13	Discriminant
Eigenvalues	2- -1 5+ 7-  3 13-  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-215111,38323683]	[a1,a2,a3,a4,a6]
j	-27279055902727/10156250	j-invariant
L	2.0891904585949	L(r)(E,1)/r!
Ω	0.52229761464871	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50960bc1 57330cw1 31850h1 6370u1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370o1

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
-	-1	+	-	3	-	0	-8	7	-2	3	-7	-9	10	3	-6	4	7	11	2	3	-3	-6	6	5

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Quadratic twists for elliptic curve 6370o1

-4	-3	5	-7	13
50960bc1	57330cw1	31850h1	6370u1	82810bh1

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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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