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	6370w	Isogeny class
Conductor	6370	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	38016	Modular degree for the optimal curve
Δ	-45152940851200 = -1 · 224 · 52 · 72 · 133	Discriminant
Eigenvalues	2-  2 5- 7-  3 13+  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-150060,-22438963]	[a1,a2,a3,a4,a6]
j	-7626453723007966609/921488588800	j-invariant
L	5.8215870727737	L(r)(E,1)/r!
Ω	0.12128306401612	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	50960bw1 57330bc1 31850bd1 6370k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370w1

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	1	-6	3	4	2	6	8	-3	3	9	-5	5	-15	4	8	12	12	4

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Quadratic twists for elliptic curve 6370w1

-4	-3	5	-7	13
50960bw1	57330bc1	31850bd1	6370k1	82810m1

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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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