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	12320j	Isogeny class
Conductor	12320	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	4096	Modular degree for the optimal curve
Δ	237160000 = 26 · 54 · 72 · 112	Discriminant
Eigenvalues	2-  0 5- 7- 11+  6  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-157,-156]	[a1,a2,a3,a4,a6]
j	6687175104/3705625	j-invariant
L	2.8901240945723	L(r)(E,1)/r!
Ω	1.4450620472862	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12320c1 24640n2 110880bq1 61600c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320j1

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	-	-	+	6	6	4	4	-6	8	6	-2	4	-8	-10	8	6	4	-4	-2	16	4	-6	-14

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Quadratic twists for elliptic curve 12320j1

-4	8	-3	5	-7
12320c1	24640n2	110880bq1	61600c1	86240x1

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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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