Cremona's table of elliptic curves

21390 = 2 · 3 · 5 · 23 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 23+ 31+	Signs for the Atkin-Lehner involutions
Class	21390r	Isogeny class
Conductor	21390	Conductor
∏ cp	320	Product of Tamagawa factors cp
Δ	850124160000 = 210 · 34 · 54 · 232 · 31	Discriminant
Eigenvalues	2- 3- 5-  4 -4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-89560410,326221280100]	[a1,a2,a3,a4,a6]
j	79445980921792374411056238241/850124160000	j-invariant
L	6.1042636460097	L(r)(E,1)/r!
Ω	0.30521318230049	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	64170k4 106950k4	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 21390r4

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	-4	2	-6	-4	+	10	+	2	10	-4	8	6	-8	14	-8	12	-10	8	-4	14	-14

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Quadratic twists for elliptic curve 21390r4

-3	5
64170k4	106950k4

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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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