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	6370bb	Isogeny class
Conductor	6370	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	-3106668906250000 = -1 · 24 · 510 · 76 · 132	Discriminant
Eigenvalues	2- -2 5- 7- -2 13- -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-37290,3853492]	[a1,a2,a3,a4,a6]
Generators	[174:-1712:1]	Generators of the group modulo torsion
j	-48743122863889/26406250000	j-invariant
L	4.4217054687775	L(r)(E,1)/r!
Ω	0.41757584452535	Real period
R	0.26472469173855	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50960cd2 57330bk2 31850m2 130c2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6370bb2

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	-	-	-2	-	-2	-6	6	2	6	-2	-10	-10	12	2	-10	-2	-12	10	-10	-4	0	14	-14

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Quadratic twists for elliptic curve 6370bb2

-4	-3	5	-7	13
50960cd2	57330bk2	31850m2	130c2	82810p2

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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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