Cremona's table of elliptic curves

34 = 2 · 17

Field	Data	Notes
Atkin-Lehner	2- 17+	Signs for the Atkin-Lehner involutions
Conductor	34	Conductor
Count	4	Number of curves in isogeny class
Curves	34a1 34a2 34a3 34a4	Curves in isogeny class
deg	2	Modular degree for the optimal curve
Eigenvalues	2- -2  0 -4  6  2 17+ -4	Hecke eigenvalues for primes less than 20
L	0.74927722105228	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	272d 1088c 306b 850b	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 34a

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
-	-2	0	-4	6	2	+	-4	0	0	-4	-4	6	8	0	-6	0	-4	8	0	2	8	0	-6	14

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Quadratic twists for isogeny class 34a

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
272d	1088c	306b	850b	1666l	4114b	5746e	578a	12274d	17986j	28594f	32674d	46546a	57154n	62866c	75106b	95506a	118354e	126514e

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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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