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	624i	Isogeny class
Conductor	624	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	2970628732551168 = 216 · 320 · 13	Discriminant
Eigenvalues	2- 3-  2 -4  4 13-  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-37432,932948]	[a1,a2,a3,a4,a6]
j	1416134368422073/725251155408	j-invariant
L	1.9891607555961	L(r)(E,1)/r!
Ω	0.39783215111923	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	78a3 2496u4 1872r3 15600bd4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624i4

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	4	-	2	8	0	6	4	-2	-10	-4	-8	-10	-4	-2	16	8	2	-8	-12	14	10

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Quadratic twists for elliptic curve 624i4

-4	8	-3	5	-7	-11	13
78a3	2496u4	1872r3	15600bd4	30576br3	75504cm3	8112bg4

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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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