Cremona's table of elliptic curves

10360 = 2³ · 5 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 37+	Signs for the Atkin-Lehner involutions
Class	10360a	Isogeny class
Conductor	10360	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	55968	Modular degree for the optimal curve
Δ	-146322178982000 = -1 · 24 · 53 · 711 · 37	Discriminant
Eigenvalues	2+ -3 5+ 7+  4  6  2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,617,-581957]	[a1,a2,a3,a4,a6]
Generators	[143:1559:1]	Generators of the group modulo torsion
j	1623525901056/9145136186375	j-invariant
L	2.6594824394108	L(r)(E,1)/r!
Ω	0.26820646907716	Real period
R	4.9579013671099	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	20720b1 82880r1 93240bx1 51800t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10360a1

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
+	-3	+	+	4	6	2	-1	-1	-2	-9	+	6	-8	3	-12	7	-3	-6	-5	2	0	-7	-6	4

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Quadratic twists for elliptic curve 10360a1

-4	8	-3	5	-7
20720b1	82880r1	93240bx1	51800t1	72520k1

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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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