Cremona's table of elliptic curves

51744 = 2⁵ · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	51744u	Isogeny class
Conductor	51744	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	18520309344768 = 29 · 3 · 77 · 114	Discriminant
Eigenvalues	2+ 3+  2 7- 11-  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-12952,-523928]	[a1,a2,a3,a4,a6]
Generators	[-4956:5965:64]	Generators of the group modulo torsion
j	3989418056/307461	j-invariant
L	6.3971196579154	L(r)(E,1)/r!
Ω	0.44970388693469	Real period
R	7.1125910224086	Regulator
r	1	Rank of the group of rational points
S	1.0000000000012	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	51744bn3 103488hw3 7392h3	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 51744u3

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	-	-	2	2	4	-8	2	-4	-2	-6	12	0	2	4	-14	8	8	-14	-16	0	-6	-2

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Quadratic twists for elliptic curve 51744u3

-4	8	-7
51744bn3	103488hw3	7392h3

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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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