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	672b	Isogeny class
Conductor	672	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-1829677248 = -1 · 26 · 35 · 76	Discriminant
Eigenvalues	2+ 3- -4 7- -2 -2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,210,1764]	[a1,a2,a3,a4,a6]
Generators	[0:42:1]	Generators of the group modulo torsion
j	15926924096/28588707	j-invariant
L	2.1403725793839	L(r)(E,1)/r!
Ω	1.0195945289441	Real period
R	0.13994926536143	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	672d1 1344e2 2016n1 16800be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 672b1

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

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Quadratic twists for elliptic curve 672b1

-4	8	-3	5	-7	-11	13
672d1	1344e2	2016n1	16800be1	4704h1	81312br1	113568cq1

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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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