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	10320a	Isogeny class
Conductor	10320	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	-325005696000 = -1 · 210 · 310 · 53 · 43	Discriminant
Eigenvalues	2+ 3+ 5+  0  0  4  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1144,22656]	[a1,a2,a3,a4,a6]
Generators	[-12:84:1]	Generators of the group modulo torsion
j	161555647964/317388375	j-invariant
L	3.6677281170118	L(r)(E,1)/r!
Ω	0.66553344563026	Real period
R	2.7554799395081	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	5160l1 41280dm1 30960g1 51600z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10320a1

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	0	4	4	0	-4	-2	-4	-6	2	+	0	-10	8	8	-8	-12	-10	-8	14	12	18

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Quadratic twists for elliptic curve 10320a1

-4	8	-3	5
5160l1	41280dm1	30960g1	51600z1

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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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