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	10320s	Isogeny class
Conductor	10320	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-11145600000000 = -1 · 213 · 34 · 58 · 43	Discriminant
Eigenvalues	2- 3+ 5+ -4  0 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,5464,38640]	[a1,a2,a3,a4,a6]
Generators	[74:918:1]	Generators of the group modulo torsion
j	4403686064471/2721093750	j-invariant
L	2.7033377611529	L(r)(E,1)/r!
Ω	0.4438099828291	Real period
R	3.0456026968121	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	1290d4 41280dk3 30960cd3 51600cx3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10320s4

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	2	-4	0	2	0	10	-6	-	8	2	0	2	4	-8	10	8	-16	6	2

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Quadratic twists for elliptic curve 10320s4

-4	8	-3	5
1290d4	41280dk3	30960cd3	51600cx3

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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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