Cremona's table of elliptic curves

26 = 2 · 13

Field	Data	Notes
Atkin-Lehner	2+ 13-	Signs for the Atkin-Lehner involutions
Class	26a	Isogeny class
Conductor	26	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-26 = -1 · 2 · 13	Discriminant
Eigenvalues	2+  1 -3 -1  6 13- -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,0,0]	[a1,a2,a3,a4,a6]
j	12167/26	j-invariant
L	0.51557665127729	L(r)(E,1)/r!
Ω	4.6401898614957	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	208a1 832c1 234e1 650h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 26a3

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	-1	6	-	-3	2	0	6	-4	-7	0	-1	3	0	-6	8	14	-3	2	8	12	-6	-10

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Quadratic twists for elliptic curve 26a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67
208a1	832c1	234e1	650h1	1274c1	3146l1	338c1	7514b1	9386g1	13754d1	21866j1	24986b1	35594d1	43706b1	48074e1	57434b1	73034k1	90506d1	96746k1	116714e1

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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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