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	12320c	Isogeny class
Conductor	12320	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2704486400 = 212 · 52 · 74 · 11	Discriminant
Eigenvalues	2+  0 5- 7+ 11-  6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1532,-22944]	[a1,a2,a3,a4,a6]
Generators	[-174:75:8]	Generators of the group modulo torsion
j	97082300736/660275	j-invariant
L	4.8921083769955	L(r)(E,1)/r!
Ω	0.76341880651248	Real period
R	3.204079029271	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	12320j3 24640b1 110880cw3 61600bp3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320c2

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 12320c2

-4	8	-3	5	-7
12320j3	24640b1	110880cw3	61600bp3	86240h3

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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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