Cremona's table of elliptic curves

57 = 3 · 19

Field	Data	Notes
Atkin-Lehner	3- 19+	Signs for the Atkin-Lehner involutions
Conductor	57	Conductor
Count	4	Number of curves in isogeny class
Curves	57b1 57b2 57b3 57b4	Curves in isogeny class
deg	3	Modular degree for the optimal curve
Eigenvalues	1 3- -2  0  0  6 -6 19+	Hecke eigenvalues for primes less than 20
L	1.0853022722677	L(r)(E,1)/r!
r	0	Rank of the group of rational points
Twists	912g 3648g 171a 1425a	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 57b

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	0	0	6	-6	+	4	2	8	-10	-2	-4	12	-6	-12	-2	-4	0	10	0	16	-2	10

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Quadratic twists for isogeny class 57b

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47
912g	3648g	171a	1425a	2793c	6897f	9633m	16473a	1083b	30153h	47937b	54777a	78033b	95817d	105393j	125913g

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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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