Cremona's table of elliptic curves

9768 = 2³ · 3 · 11 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 37-	Signs for the Atkin-Lehner involutions
Class	9768f	Isogeny class
Conductor	9768	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	5376	Modular degree for the optimal curve
Δ	5597611008 = 210 · 3 · 113 · 372	Discriminant
Eigenvalues	2+ 3+  2  2 11- -2 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1232,16668]	[a1,a2,a3,a4,a6]
Generators	[-14:176:1]	Generators of the group modulo torsion
j	202119559492/5466417	j-invariant
L	4.60213190871	L(r)(E,1)/r!
Ω	1.3484697823906	Real period
R	1.1376183505206	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19536k1 78144bb1 29304k1 107448q1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 9768f1

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	-2	2	-8	-2	0	-	10	6	-2	-4	-10	-10	-4	-2	-14	4	-4	-12	2

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Quadratic twists for elliptic curve 9768f1

-4	8	-3	-11
19536k1	78144bb1	29304k1	107448q1

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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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