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	12320f	Isogeny class
Conductor	12320	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	6678425600 = 212 · 52 · 72 · 113	Discriminant
Eigenvalues	2-  0 5- 7+ 11+ -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-7052,-227904]	[a1,a2,a3,a4,a6]
Generators	[272:4240:1]	Generators of the group modulo torsion
j	9468924964416/1630475	j-invariant
L	4.4512627326459	L(r)(E,1)/r!
Ω	0.52098589580906	Real period
R	4.271960880758	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	12320l2 24640bf1 110880bd2 61600j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320f2

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

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Quadratic twists for elliptic curve 12320f2

-4	8	-3	5	-7
12320l2	24640bf1	110880bd2	61600j2	86240u2

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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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