Cremona's table of elliptic curves

12376 = 2³ · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 7- 13- 17+	Signs for the Atkin-Lehner involutions
Class	12376f	Isogeny class
Conductor	12376	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	27328	Modular degree for the optimal curve
Δ	-259973631776768 = -1 · 211 · 7 · 137 · 172	Discriminant
Eigenvalues	2+  1 -2 7-  3 13- 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-824,-776080]	[a1,a2,a3,a4,a6]
Generators	[2266:37349:8]	Generators of the group modulo torsion
j	-30248395634/126940249891	j-invariant
L	4.9744643719895	L(r)(E,1)/r!
Ω	0.25082776091645	Real period
R	1.4165851595346	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24752g1 99008w1 111384co1 86632e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12376f1

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
+	1	-2	-	3	-	+	0	-1	-4	5	7	-5	2	7	-12	-4	-1	5	6	-9	1	4	-6	13

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Quadratic twists for elliptic curve 12376f1

-4	8	-3	-7
24752g1	99008w1	111384co1	86632e1

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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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