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	672a	Isogeny class
Conductor	672	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	258048 = 212 · 32 · 7	Discriminant
Eigenvalues	2+ 3+  0 7+ -2 -2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-33,81]	[a1,a2,a3,a4,a6]
Generators	[-3:12:1]	Generators of the group modulo torsion
j	1000000/63	j-invariant
L	1.8770484001592	L(r)(E,1)/r!
Ω	3.0552339984409	Real period
R	0.30718570183447	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	672g2 1344f1 2016k2 16800bw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 672a2

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
+	+	0	+	-2	-2	4	-4	-6	-2	0	-6	8	-8	-4	-6	0	-14	4	-2	-2	4	12	0	6

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Quadratic twists for elliptic curve 672a2

-4	8	-3	5	-7	-11	13
672g2	1344f1	2016k2	16800bw2	4704l2	81312bd2	113568bw2

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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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