Cremona's table of elliptic curves

12705 = 3 · 5 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Conductor	12705	Conductor
Count	1	Number of curves in isogeny class
Curves	12705a1	Curves in isogeny class
deg	48000	Modular degree for the optimal curve
Eigenvalues	0 3+ 5+ 7+ 11-  0 -3  3	Hecke eigenvalues for primes less than 20
L	0.76435584412365	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	38115w 63525bq 88935ce 1155d	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for isogeny class 12705a

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	+	+	+	-	0	-3	3	-1	7	6	-8	2	5	-6	-3	-5	7	6	-10	-12	16	3	3	-1

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Quadratic twists for isogeny class 12705a

-3	5	-7	-11
38115w	63525bq	88935ce	1155d

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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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