Cremona's table of elliptic curves

624 = 2⁴ · 3 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 13-	Signs for the Atkin-Lehner involutions
Class	624f	Isogeny class
Conductor	624	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	87340032 = 210 · 38 · 13	Discriminant
Eigenvalues	2+ 3- -2 -4  0 13-  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-304,1892]	[a1,a2,a3,a4,a6]
Generators	[-16:54:1]	Generators of the group modulo torsion
j	3044193988/85293	j-invariant
L	2.1165060726217	L(r)(E,1)/r!
Ω	1.9064113549902	Real period
R	0.55510214704755	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	312d3 2496s3 1872h3 15600e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624f3

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	-4	0	-	2	-8	-8	-2	-4	-10	2	4	12	6	0	-2	-8	12	10	8	0	-14	2

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Quadratic twists for elliptic curve 624f3

-4	8	-3	5	-7	-11	13
312d3	2496s3	1872h3	15600e3	30576c4	75504s4	8112m3

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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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