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	12	Product of Tamagawa factors cp
Δ	-25533508608 = -1 · 210 · 33 · 314	Discriminant
Eigenvalues	2+ 3- -2  0  4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,256,-7440]	[a1,a2,a3,a4,a6]
j	1804870652/24935067	j-invariant
L	1.7517021682135	L(r)(E,1)/r!
Ω	0.58390072273782	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	1488c4 5952c4 2232k4 18600p4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 744b4

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 744b4

-4	8	-3	5	-7	-11	13	-31
1488c4	5952c4	2232k4	18600p4	36456h3	90024ba3	125736y3	23064b3

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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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