Cremona's table of elliptic curves

1624 = 2³ · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 7- 29+	Signs for the Atkin-Lehner involutions
Class	1624d	Isogeny class
Conductor	1624	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	3493704704 = 210 · 76 · 29	Discriminant
Eigenvalues	2- -2 -2 7-  0  2  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-504,3136]	[a1,a2,a3,a4,a6]
Generators	[0:56:1]	Generators of the group modulo torsion
j	13854050788/3411821	j-invariant
L	1.9174875088569	L(r)(E,1)/r!
Ω	1.3201087076566	Real period
R	0.48417414357255	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3248a2 12992s2 14616e2 40600a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1624d2

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

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Quadratic twists for elliptic curve 1624d2

-4	8	-3	5	-7	29
3248a2	12992s2	14616e2	40600a2	11368l2	47096e2

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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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