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	3	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	-17576 = -1 · 23 · 133	Discriminant
Eigenvalues	2+  1 -3 -1  6 13- -3  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-5,-8]	[a1,a2,a3,a4,a6]
j	-10218313/17576	j-invariant
L	0.51557665127729	L(r)(E,1)/r!
Ω	1.5467299538319	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	208a2 832c2 234e2 650h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 26a1

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 26a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67
208a2	832c2	234e2	650h2	1274c2	3146l2	338c2	7514b2	9386g2	13754d2	21866j2	24986b2	35594d2	43706b2	48074e2	57434b2	73034k2	90506d2	96746k2	116714e2

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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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