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	10320b	Isogeny class
Conductor	10320	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-1030410720000 = -1 · 28 · 34 · 54 · 433	Discriminant
Eigenvalues	2+ 3+ 5+  2  3  3  1  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-721,49645]	[a1,a2,a3,a4,a6]
Generators	[28:225:1]	Generators of the group modulo torsion
j	-162140591104/4025041875	j-invariant
L	4.1336027402082	L(r)(E,1)/r!
Ω	0.73398897405231	Real period
R	1.4079239901203	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5160f1 41280do1 30960j1 51600ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10320b1

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	3	3	1	2	-1	0	-9	-12	1	+	-8	-5	-12	-12	13	6	-8	8	3	-10	-1

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Quadratic twists for elliptic curve 10320b1

-4	8	-3	5
5160f1	41280do1	30960j1	51600ba1

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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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