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	2352r	Isogeny class
Conductor	2352	Conductor
∏ cp	84	Product of Tamagawa factors cp
Δ	-6610023762886656 = -1 · 219 · 37 · 78	Discriminant
Eigenvalues	2- 3-  1 7+ -5  0 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-110560,14643572]	[a1,a2,a3,a4,a6]
Generators	[506:9408:1]	Generators of the group modulo torsion
j	-6329617441/279936	j-invariant
L	3.7316897839152	L(r)(E,1)/r!
Ω	0.41804097115226	Real period
R	0.10626919714949	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	294a2 9408bp2 7056bk2 58800fa2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2352r2

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

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Quadratic twists for elliptic curve 2352r2

-4	8	-3	5	-7
294a2	9408bp2	7056bk2	58800fa2	2352l2

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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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