Cremona's table of elliptic curves

6390 = 2 · 3² · 5 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 71-	Signs for the Atkin-Lehner involutions
Class	6390i	Isogeny class
Conductor	6390	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2778767317350 = 2 · 37 · 52 · 714	Discriminant
Eigenvalues	2+ 3- 5+ -4  0  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-8145,273375]	[a1,a2,a3,a4,a6]
Generators	[-99:369:1]	Generators of the group modulo torsion
j	81978400815121/3811752150	j-invariant
L	2.3367903747694	L(r)(E,1)/r!
Ω	0.79735123009834	Real period
R	0.73267284433773	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	51120ba3 2130o3 31950co3	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6390i4

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
+	-	+	-4	0	2	-6	4	0	2	4	6	2	-4	0	-6	0	2	12	-	-6	0	4	-2	10

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Quadratic twists for elliptic curve 6390i4

-4	-3	5
51120ba3	2130o3	31950co3

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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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