Cremona's table of elliptic curves

17 = Prime conductor

Field	Data	Notes
Atkin-Lehner	17-	Signs for the Atkin-Lehner involutions
Conductor	17	Conductor
Count	4	Number of curves in isogeny class
Curves	17a1 17a2 17a3 17a4	Curves in isogeny class
deg	1	Modular degree for the optimal curve
Eigenvalues	-1  0 -2  4  0 -2 17- -4	Hecke eigenvalues for primes less than 20
L	0.38676993838778	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	272b 1088e 153c 425a	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 17a

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	0	-2	4	0	-2	-	-4	4	6	4	-2	-6	4	0	6	-12	-10	4	-4	-6	12	-4	10	2

---

Quadratic twists for isogeny class 17a

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61	-67	-71	73	-79	-83
272b	1088e	153c	425a	833a	2057c	2873a	289a	6137b	8993a	14297a	16337a	23273b	28577a	31433b	37553a	47753f	59177b	63257a	76313b	85697a	90593a	106097a	117113c

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations