Cremona's table of elliptic curves

10350 = 2 · 3² · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 23+	Signs for the Atkin-Lehner involutions
Class	10350bi	Isogeny class
Conductor	10350	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-92553840000000 = -1 · 210 · 37 · 57 · 232	Discriminant
Eigenvalues	2- 3- 5+  0  2 -4  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-55130,5017497]	[a1,a2,a3,a4,a6]
Generators	[89:855:1]	Generators of the group modulo torsion
j	-1626794704081/8125440	j-invariant
L	6.7833704727447	L(r)(E,1)/r!
Ω	0.60532502346182	Real period
R	0.28015405814347	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	82800dt1 3450c1 2070e1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 10350bi1

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	2	-4	6	-8	+	-4	0	2	2	-2	-12	-6	-8	2	6	-10	2	-8	8	12	16

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Quadratic twists for elliptic curve 10350bi1

-4	-3	5
82800dt1	3450c1	2070e1

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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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