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	672c	Isogeny class
Conductor	672	Conductor
∏ cp	4	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	1.4729892849024	L(r)(E,1)/r!
Ω	1.4729892849024	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	672h3 1344q3 2016d3 16800u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 672c2

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 672c2

-4	8	-3	5	-7	-11	13
672h3	1344q3	2016d3	16800u2	4704be3	81312l3	113568s3

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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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