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	4	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	22736 = 24 · 72 · 29	Discriminant
Eigenvalues	2-  2  2 7+  0  6  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7,0]	[a1,a2,a3,a4,a6]
j	2725888/1421	j-invariant
L	3.0725081511262	L(r)(E,1)/r!
Ω	3.0725081511262	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	3248e1 12992h1 14616c1 40600f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1624c1

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 1624c1

-4	8	-3	5	-7	29
3248e1	12992h1	14616c1	40600f1	11368m1	47096c1

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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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