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	6370ba	Isogeny class
Conductor	6370	Conductor
∏ cp	264	Product of Tamagawa factors cp
deg	8448	Modular degree for the optimal curve
Δ	-964570880000 = -1 · 211 · 54 · 73 · 133	Discriminant
Eigenvalues	2- -1 5- 7- -1 13- -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4075,109017]	[a1,a2,a3,a4,a6]
Generators	[-43:476:1]	Generators of the group modulo torsion
j	-21818208730807/2812160000	j-invariant
L	5.1732919773195	L(r)(E,1)/r!
Ω	0.85408669222013	Real period
R	0.022943576012705	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50960cb1 57330bj1 31850g1 6370m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370ba1

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	-	-	-1	-	-4	0	-1	-6	7	5	7	-2	-5	-14	-8	-1	-13	-6	7	1	-2	-10	9

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Quadratic twists for elliptic curve 6370ba1

-4	-3	5	-7	13
50960cb1	57330bj1	31850g1	6370m1	82810j1

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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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