Cremona's table of elliptic curves

4026 = 2 · 3 · 11 · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 61-	Signs for the Atkin-Lehner involutions
Class	4026h	Isogeny class
Conductor	4026	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1248	Modular degree for the optimal curve
Δ	-7826544 = -1 · 24 · 36 · 11 · 61	Discriminant
Eigenvalues	2- 3+  2  4 11-  2  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-22,131]	[a1,a2,a3,a4,a6]
j	-1180932193/7826544	j-invariant
L	4.0289473396071	L(r)(E,1)/r!
Ω	2.0144736698036	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	32208o1 128832o1 12078i1 100650ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4026h1

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

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Quadratic twists for elliptic curve 4026h1

-4	8	-3	5	-11
32208o1	128832o1	12078i1	100650ba1	44286a1

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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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