Cremona's table of elliptic curves

26208 = 2⁵ · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	26208bc	Isogeny class
Conductor	26208	Conductor
∏ cp	44	Product of Tamagawa factors cp
deg	689920	Modular degree for the optimal curve
Δ	-173423777010172416 = -1 · 29 · 33 · 7 · 1311	Discriminant
Eigenvalues	2- 3+ -3 7+  3 13-  7 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2244219,1294189934]	[a1,a2,a3,a4,a6]
Generators	[805:3042:1]	Generators of the group modulo torsion
j	-90424411632287643672/12545122758259	j-invariant
L	4.4990552307027	L(r)(E,1)/r!
Ω	0.30999435670402	Real period
R	0.32984876347563	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26208f1 52416k1 26208c1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 26208bc1

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
-	+	-3	+	3	-	7	-1	9	3	-10	-3	-10	-1	-8	-14	6	-3	8	-10	-1	-10	10	10	18

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Quadratic twists for elliptic curve 26208bc1

-4	8	-3
26208f1	52416k1	26208c1

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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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