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	10320p	Isogeny class
Conductor	10320	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	69120	Modular degree for the optimal curve
Δ	138669096960000 = 218 · 39 · 54 · 43	Discriminant
Eigenvalues	2- 3+ 5+ -2  0  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-281056,-57254144]	[a1,a2,a3,a4,a6]
j	599437478278595809/33854760000	j-invariant
L	0.41469870390957	L(r)(E,1)/r!
Ω	0.20734935195479	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1290n1 41280dp1 30960bw1 51600dh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10320p1

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

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Quadratic twists for elliptic curve 10320p1

-4	8	-3	5
1290n1	41280dp1	30960bw1	51600dh1

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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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