Cremona's table of elliptic curves

2352 = 2⁴ · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+	Signs for the Atkin-Lehner involutions
Class	2352f	Isogeny class
Conductor	2352	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-39846304512 = -1 · 28 · 33 · 78	Discriminant
Eigenvalues	2+ 3-  2 7+  6 -3  4  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-457,10163]	[a1,a2,a3,a4,a6]
j	-7168/27	j-invariant
L	3.0116848280294	L(r)(E,1)/r!
Ω	1.0038949426765	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	1176a1 9408br1 7056p1 58800m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2352f1

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
+	-	2	+	6	-3	4	5	4	-4	-7	-9	-2	1	-2	8	0	10	15	6	-11	-1	-6	-8	-14

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Quadratic twists for elliptic curve 2352f1

-4	8	-3	5	-7
1176a1	9408br1	7056p1	58800m1	2352e1

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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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