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	12320a	Isogeny class
Conductor	12320	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1024	Modular degree for the optimal curve
Δ	-172480 = -1 · 26 · 5 · 72 · 11	Discriminant
Eigenvalues	2+ -2 5+ 7- 11- -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,14,0]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	4410944/2695	j-invariant
L	2.7357471119378	L(r)(E,1)/r!
Ω	1.862408328277	Real period
R	1.4689298100749	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	12320e1 24640v1 110880dt1 61600bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320a1

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

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Quadratic twists for elliptic curve 12320a1

-4	8	-3	5	-7
12320e1	24640v1	110880dt1	61600bj1	86240p1

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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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