Cremona's table of elliptic curves

744 = 2³ · 3 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 31+	Signs for the Atkin-Lehner involutions
Class	744b	Isogeny class
Conductor	744	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	16870063104 = 210 · 312 · 31	Discriminant
Eigenvalues	2+ 3- -2  0  4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-904,8096]	[a1,a2,a3,a4,a6]
j	79874724388/16474671	j-invariant
L	1.7517021682135	L(r)(E,1)/r!
Ω	1.1678014454756	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1488c3 5952c3 2232k3 18600p3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 744b3

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

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Quadratic twists for elliptic curve 744b3

-4	8	-3	5	-7	-11	13	-31
1488c3	5952c3	2232k3	18600p3	36456h4	90024ba4	125736y4	23064b4

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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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