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	672d	Isogeny class
Conductor	672	Conductor
∏ cp	4	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]
j	15926924096/28588707	j-invariant
L	0.77847339872192	L(r)(E,1)/r!
Ω	0.77847339872192	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	672b1 1344h2 2016e1 16800v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 672d1

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 672d1

-4	8	-3	5	-7	-11	13
672b1	1344h2	2016e1	16800v1	4704bg1	81312o1	113568w1

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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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