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	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]
Generators	[-8:30:1]	Generators of the group modulo torsion
j	6687175104/3705625	j-invariant
L	4.8921083769955	L(r)(E,1)/r!
Ω	1.526837613025	Real period
R	1.6020395146355	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	12320j1 24640b2 110880cw1 61600bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320c1

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 12320c1

-4	8	-3	5	-7
12320j1	24640b2	110880cw1	61600bp1	86240h1

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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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