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	6370r	Isogeny class
Conductor	6370	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2496	Modular degree for the optimal curve
Δ	-32461520 = -1 · 24 · 5 · 74 · 132	Discriminant
Eigenvalues	2-  1 5- 7+ -4 13+  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-295,1945]	[a1,a2,a3,a4,a6]
Generators	[12:7:1]	Generators of the group modulo torsion
j	-1182740881/13520	j-invariant
L	6.8986479624583	L(r)(E,1)/r!
Ω	2.0863813384396	Real period
R	0.41331418155429	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	50960bh1 57330o1 31850d1 6370p1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370r1

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	-	+	-4	+	0	-6	7	-9	4	0	-5	-11	4	-6	-4	7	11	-12	4	4	-15	-13	2

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Quadratic twists for elliptic curve 6370r1

-4	-3	5	-7	13
50960bh1	57330o1	31850d1	6370p1	82810b1

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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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