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	16	Product of Tamagawa factors cp
Δ	1311833600 = 29 · 52 · 7 · 114	Discriminant
Eigenvalues	2+  0 5- 7+ 11-  6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1907,32006]	[a1,a2,a3,a4,a6]
Generators	[62:390:1]	Generators of the group modulo torsion
j	1497979362888/2562175	j-invariant
L	4.8921083769955	L(r)(E,1)/r!
Ω	1.526837613025	Real period
R	3.204079029271	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12320j2 24640b4 110880cw4 61600bp4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320c3

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 12320c3

-4	8	-3	5	-7
12320j2	24640b4	110880cw4	61600bp4	86240h4

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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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