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	12320i	Isogeny class
Conductor	12320	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-19841483200 = -1 · 26 · 52 · 7 · 116	Discriminant
Eigenvalues	2- -2 5- 7+ 11- -4 -8 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-210,6808]	[a1,a2,a3,a4,a6]
Generators	[2:80:1] [21:110:1]	Generators of the group modulo torsion
j	-16079333824/310023175	j-invariant
L	4.9352520165071	L(r)(E,1)/r!
Ω	1.0246725224515	Real period
R	0.8027364691924	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12320d1 24640d2 110880z1 61600q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320i1

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	-8	-8	-4	-2	-2	-6	-12	-4	6	-6	-6	-12	4	-16	4	0	16	-6	-18

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Quadratic twists for elliptic curve 12320i1

-4	8	-3	5	-7
12320d1	24640d2	110880z1	61600q1	86240bm1

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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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