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	6370a	Isogeny class
Conductor	6370	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	5184	Modular degree for the optimal curve
Δ	-2109998800 = -1 · 24 · 52 · 74 · 133	Discriminant
Eigenvalues	2+ -2 5+ 7+ -3 13- -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-369,3476]	[a1,a2,a3,a4,a6]
Generators	[-22:43:1] [-17:78:1]	Generators of the group modulo torsion
j	-2305248169/878800	j-invariant
L	2.8720398893782	L(r)(E,1)/r!
Ω	1.3793833369474	Real period
R	0.5205296838899	Regulator
r	2	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	50960q1 57330et1 31850bn1 6370i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370a1

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	+	+	-3	-	-3	-7	-6	-9	-4	-10	6	-4	9	-9	9	-7	-13	3	-4	8	-12	0	-16

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Quadratic twists for elliptic curve 6370a1

-4	-3	5	-7	13
50960q1	57330et1	31850bn1	6370i1	82810ch1

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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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