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	16	Product of Tamagawa factors cp
Δ	11063808 = 29 · 32 · 74	Discriminant
Eigenvalues	2- 3-  2 7-  0  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-112,392]	[a1,a2,a3,a4,a6]
j	306182024/21609	j-invariant
L	2.2280058144292	L(r)(E,1)/r!
Ω	2.2280058144292	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	672c2 1344n3 2016h2 16800a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 672h3

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 672h3

-4	8	-3	5	-7	-11	13
672c2	1344n3	2016h2	16800a3	4704v2	81312t3	113568bc3

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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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