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	672g	Isogeny class
Conductor	672	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-9408 = -1 · 26 · 3 · 72	Discriminant
Eigenvalues	2- 3-  0 7-  2 -2  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,2,-4]	[a1,a2,a3,a4,a6]
j	8000/147	j-invariant
L	1.9947625015733	L(r)(E,1)/r!
Ω	1.9947625015733	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	672a1 1344c2 2016f1 16800b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 672g1

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 672g1

-4	8	-3	5	-7	-11	13
672a1	1344c2	2016f1	16800b1	4704s1	81312q1	113568x1

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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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