Cremona's table of elliptic curves

644 = 2² · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 7- 23+	Signs for the Atkin-Lehner involutions
Class	644b	Isogeny class
Conductor	644	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-18032 = -1 · 24 · 72 · 23	Discriminant
Eigenvalues	2- -1  0 7- -2 -3  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2,-7]	[a1,a2,a3,a4,a6]
Generators	[4:7:1]	Generators of the group modulo torsion
j	32000/1127	j-invariant
L	1.866603424807	L(r)(E,1)/r!
Ω	1.8677219380527	Real period
R	0.16656685583803	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2576m1 10304i1 5796g1 16100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 644b1

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
-	-1	0	-	-2	-3	0	0	+	1	-5	-8	-7	-4	3	-12	4	-6	-12	13	3	4	16	4	10

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Quadratic twists for elliptic curve 644b1

-4	8	-3	5	-7	-11	13	-23
2576m1	10304i1	5796g1	16100b1	4508a1	77924e1	108836b1	14812a1

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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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