Cremona's table of elliptic curves

12390 = 2 · 3 · 5 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7+ 59-	Signs for the Atkin-Lehner involutions
Class	12390h	Isogeny class
Conductor	12390	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	3.9620937716992E+19	Discriminant
Eigenvalues	2+ 3- 5+ 7+  4  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8635684,-9763743454]	[a1,a2,a3,a4,a6]
Generators	[3688:90638:1]	Generators of the group modulo torsion
j	71221950981500494702291129/39620937716991590400	j-invariant
L	4.1914080840153	L(r)(E,1)/r!
Ω	0.088072409138982	Real period
R	4.7590478391491	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	99120bm2 37170bh2 61950br2 86730p2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12390h2

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

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Quadratic twists for elliptic curve 12390h2

-4	-3	5	-7
99120bm2	37170bh2	61950br2	86730p2

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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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