Cremona's table of elliptic curves

10320 = 2⁴ · 3 · 5 · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 43+	Signs for the Atkin-Lehner involutions
Class	10320o	Isogeny class
Conductor	10320	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	367505463066624000 = 217 · 38 · 53 · 434	Discriminant
Eigenvalues	2- 3+ 5+  0 -4 -6 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-391256,89698800]	[a1,a2,a3,a4,a6]
j	1617141066657115609/89723013444000	j-invariant
L	0.59488534859876	L(r)(E,1)/r!
Ω	0.29744267429938	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1290e3 41280dn3 30960bu3 51600db3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10320o4

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
-	+	+	0	-4	-6	-6	8	4	10	0	-6	-6	+	-12	-6	4	-6	-4	-8	-10	8	12	2	10

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Quadratic twists for elliptic curve 10320o4

-4	8	-3	5
1290e3	41280dn3	30960bu3	51600db3

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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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