Cremona's table of elliptic curves

672 = 2⁵ · 3 · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 7+	Signs for the Atkin-Lehner involutions
Class	672f	Isogeny class
Conductor	672	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-3687936 = -1 · 29 · 3 · 74	Discriminant
Eigenvalues	2- 3- -2 7+ -4 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,16,-84]	[a1,a2,a3,a4,a6]
Generators	[42:105:8]	Generators of the group modulo torsion
j	830584/7203	j-invariant
L	2.2099943157884	L(r)(E,1)/r!
Ω	1.2336055843599	Real period
R	3.5829836437309	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	672e4 1344k4 2016c4 16800k4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 672f4

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

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Quadratic twists for elliptic curve 672f4

-4	8	-3	5	-7	-11	13
672e4	1344k4	2016c4	16800k4	4704u4	81312x2	113568bo2

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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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