Cremona's table of elliptic curves

26800 = 2⁴ · 5² · 67

Field	Data	Notes
Atkin-Lehner	2+ 5+ 67-	Signs for the Atkin-Lehner involutions
Class	26800j	Isogeny class
Conductor	26800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	20736	Modular degree for the optimal curve
Δ	-2093750000 = -1 · 24 · 59 · 67	Discriminant
Eigenvalues	2+ -3 5+  1 -2  2  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-175,-2375]	[a1,a2,a3,a4,a6]
j	-2370816/8375	j-invariant
L	1.2046372136392	L(r)(E,1)/r!
Ω	0.60231860681969	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13400m1 107200ch1 5360e1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 26800j1

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	+	1	-2	2	4	0	-8	5	8	-6	12	-7	12	7	-3	8	-	12	-10	10	-12	-15	5

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Quadratic twists for elliptic curve 26800j1

-4	8	5
13400m1	107200ch1	5360e1

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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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