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	624j	Isogeny class
Conductor	624	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	129792 = 28 · 3 · 132	Discriminant
Eigenvalues	2- 3- -4  2  4 13-  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-20,24]	[a1,a2,a3,a4,a6]
j	3631696/507	j-invariant
L	1.5821867465249	L(r)(E,1)/r!
Ω	3.1643734930499	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	156a2 2496v2 1872t2 15600ba2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624j2

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
-	-	-4	2	4	-	2	2	0	-6	10	10	8	-4	4	-10	8	-14	-2	-16	-10	16	0	-4	-2

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Quadratic twists for elliptic curve 624j2

-4	8	-3	5	-7	-11	13
156a2	2496v2	1872t2	15600ba2	30576bw2	75504ct2	8112bi2

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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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