Cremona's table of elliptic curves

754 = 2 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2+ 13- 29+	Signs for the Atkin-Lehner involutions
Class	754a	Isogeny class
Conductor	754	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-61861625384 = -1 · 23 · 13 · 296	Discriminant
Eigenvalues	2+  1  3 -1  0 13-  3  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,338,11752]	[a1,a2,a3,a4,a6]
j	4288639501223/61861625384	j-invariant
L	1.642581500116	L(r)(E,1)/r!
Ω	0.821290750058	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6032e2 24128f2 6786t2 18850o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 754a2

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	3	-1	0	-	3	8	6	+	-4	5	-6	11	-3	0	12	2	-10	9	-16	2	-6	6	-10

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Quadratic twists for elliptic curve 754a2

-4	8	-3	5	-7	-11	13	29
6032e2	24128f2	6786t2	18850o2	36946c2	91234t2	9802d2	21866i2

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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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