Cremona's table of elliptic curves

12320 = 2⁵ · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 11+	Signs for the Atkin-Lehner involutions
Class	12320k	Isogeny class
Conductor	12320	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	87040	Modular degree for the optimal curve
Δ	19928242069440320 = 26 · 5 · 74 · 1110	Discriminant
Eigenvalues	2- -2 5- 7- 11+ -4  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-69690,-2026532]	[a1,a2,a3,a4,a6]
j	584872717700154304/311378782335005	j-invariant
L	1.248900337552	L(r)(E,1)/r!
Ω	0.312225084388	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	12320h1 24640bp2 110880bn1 61600d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320k1

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

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Quadratic twists for elliptic curve 12320k1

-4	8	-3	5	-7
12320h1	24640bp2	110880bn1	61600d1	86240bc1

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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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