Cremona's table of elliptic curves

338 = 2 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 13+	Signs for the Atkin-Lehner involutions
Conductor	338	Conductor
Count	2	Number of curves in isogeny class
Curves	338a1 338a2	Curves in isogeny class
deg	12	Modular degree for the optimal curve
Eigenvalues	2+  0  1 -4 -4 13+  3  0	Hecke eigenvalues for primes less than 20
L	1.2776773619189	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	2704d 10816b 3042l 8450o	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 338a

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
+	0	1	-4	-4	+	3	0	-4	-1	-4	-3	9	-8	8	-9	4	7	-4	8	-11	-4	0	6	-2

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Quadratic twists for isogeny class 338a

-4	8	-3	5	-7	-11	13	17	-19
2704d	10816b	3042l	8450o	16562d	40898bg	338b	97682a	122018bb

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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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