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	6370m	Isogeny class
Conductor	6370	Conductor
∏ cp	44	Product of Tamagawa factors cp
deg	59136	Modular degree for the optimal curve
Δ	-113480799461120000 = -1 · 211 · 54 · 79 · 133	Discriminant
Eigenvalues	2-  1 5+ 7- -1 13+  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-199676,-37991920]	[a1,a2,a3,a4,a6]
Generators	[788:16756:1]	Generators of the group modulo torsion
j	-21818208730807/2812160000	j-invariant
L	6.3912700378715	L(r)(E,1)/r!
Ω	0.11211768643851	Real period
R	1.2955684498897	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	50960w1 57330cf1 31850x1 6370ba1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370m1

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 6370m1

-4	-3	5	-7	13
50960w1	57330cf1	31850x1	6370ba1	82810bd1

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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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