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	1624c	Isogeny class
Conductor	1624	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1507072 = -1 · 28 · 7 · 292	Discriminant
Eigenvalues	2-  2  2 7+  0  6  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,28,-28]	[a1,a2,a3,a4,a6]
j	9148592/5887	j-invariant
L	3.0725081511262	L(r)(E,1)/r!
Ω	1.5362540755631	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	3248e2 12992h2 14616c2 40600f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1624c2

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

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Quadratic twists for elliptic curve 1624c2

-4	8	-3	5	-7	29
3248e2	12992h2	14616c2	40600f2	11368m2	47096c2

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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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