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	10320n	Isogeny class
Conductor	10320	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	743040000 = 210 · 33 · 54 · 43	Discriminant
Eigenvalues	2+ 3- 5- -2  4 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-320,1668]	[a1,a2,a3,a4,a6]
Generators	[-14:60:1]	Generators of the group modulo torsion
j	3550014724/725625	j-invariant
L	5.4741808626356	L(r)(E,1)/r!
Ω	1.5154986759759	Real period
R	0.30101097796024	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	5160c1 41280cd1 30960d1 51600i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10320n1

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
+	-	-	-2	4	-6	2	0	-6	-2	-4	0	6	+	10	0	4	-12	4	0	-2	-16	12	-6	-18

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Quadratic twists for elliptic curve 10320n1

-4	8	-3	5
5160c1	41280cd1	30960d1	51600i1

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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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