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	16	Product of Tamagawa factors cp
Δ	2322432 = 212 · 34 · 7	Discriminant
Eigenvalues	2- 3- -2 7+ -4 -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-49,95]	[a1,a2,a3,a4,a6]
Generators	[-7:12:1]	Generators of the group modulo torsion
j	3241792/567	j-invariant
L	2.2099943157884	L(r)(E,1)/r!
Ω	2.4672111687199	Real period
R	0.89574591093274	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	672e2 1344k1 2016c2 16800k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 672f3

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 672f3

-4	8	-3	5	-7	-11	13
672e2	1344k1	2016c2	16800k3	4704u2	81312x3	113568bo3

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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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