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	12376a	Isogeny class
Conductor	12376	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4160	Modular degree for the optimal curve
Δ	-950872832 = -1 · 28 · 75 · 13 · 17	Discriminant
Eigenvalues	2+  1  2 7+ -3 13- 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,188,1168]	[a1,a2,a3,a4,a6]
j	2855256752/3714347	j-invariant
L	2.1097853283695	L(r)(E,1)/r!
Ω	1.0548926641847	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24752l1 99008c1 111384bx1 86632f1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 12376a1

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	-	+	-5	-2	-8	10	3	2	5	3	9	-4	-2	8	0	0	4	15	5	10

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Quadratic twists for elliptic curve 12376a1

-4	8	-3	-7
24752l1	99008c1	111384bx1	86632f1

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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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