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	672h	Isogeny class
Conductor	672	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-23514624 = -1 · 29 · 38 · 7	Discriminant
Eigenvalues	2- 3-  2 7-  0  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,48,-180]	[a1,a2,a3,a4,a6]
j	23393656/45927	j-invariant
L	2.2280058144292	L(r)(E,1)/r!
Ω	1.1140029072146	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	672c4 1344n4 2016h4 16800a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 672h4

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	-	0	2	2	-4	0	6	0	6	-6	-8	-8	6	12	10	-16	8	-6	-8	12	-14	-6

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Quadratic twists for elliptic curve 672h4

-4	8	-3	5	-7	-11	13
672c4	1344n4	2016h4	16800a4	4704v4	81312t2	113568bc2

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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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