Cremona's table of elliptic curves

40768 = 2⁶ · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 7- 13-	Signs for the Atkin-Lehner involutions
Class	40768bk	Isogeny class
Conductor	40768	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	193536	Modular degree for the optimal curve
Δ	48884036690944 = 210 · 710 · 132	Discriminant
Eigenvalues	2+  1 -3 7- -3 13- -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-137657,-19701361]	[a1,a2,a3,a4,a6]
Generators	[-288002:35293:1331]	Generators of the group modulo torsion
j	997335808/169	j-invariant
L	4.3382313652332	L(r)(E,1)/r!
Ω	0.24785868006818	Real period
R	8.7514211002084	Regulator
r	1	Rank of the group of rational points
S	0.99999999999913	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40768dq1 2548f1 40768c1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 40768bk1

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	-	-3	-	-3	5	-9	6	1	7	-6	-8	3	9	-9	11	13	0	7	-1	-12	3	-2

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Quadratic twists for elliptic curve 40768bk1

-4	8	-7
40768dq1	2548f1	40768c1

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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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