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	4	Number of curves in isogeny class
Curves	12705b1 12705b2 12705b3 12705b4	Curves in isogeny class
deg	34560	Modular degree for the optimal curve
Eigenvalues	-1 3+ 5+ 7+ 11-  2 -6 -4	Hecke eigenvalues for primes less than 20
L	3.554312616977	L(r)(E,1)/r!
r	2	Rank of the group of rational points
Twists	38115z 63525br 88935ci 1155c	Quadratic twists by: -3 5 -7 -11

Hecke Eigenvalues for isogeny class 12705b

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	+	+	+	-	2	-6	-4	-4	-10	-4	-2	-10	-12	0	10	-12	2	4	8	14	-4	-8	6	-10

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Quadratic twists for isogeny class 12705b

-3	5	-7	-11
38115z	63525br	88935ci	1155c

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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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