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	10320r	Isogeny class
Conductor	10320	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-35776627015680 = -1 · 216 · 310 · 5 · 432	Discriminant
Eigenvalues	2- 3+ 5+  4  2 -6 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3344,-279104]	[a1,a2,a3,a4,a6]
Generators	[1398:4690:27]	Generators of the group modulo torsion
j	1009328859791/8734528080	j-invariant
L	3.9734742001353	L(r)(E,1)/r!
Ω	0.32282376444943	Real period
R	6.1542467403415	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	1290m2 41280di2 30960cb2 51600cy2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10320r2

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	2	-6	-4	2	4	-2	-8	4	6	-	4	0	-2	-2	4	-4	-16	0	-16	-14	-10

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Quadratic twists for elliptic curve 10320r2

-4	8	-3	5
1290m2	41280di2	30960cb2	51600cy2

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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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