Cremona's table of elliptic curves

56355 = 3 · 5 · 13 · 17²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13- 17+	Signs for the Atkin-Lehner involutions
Conductor	56355	Conductor
Count	8	Number of curves in isogeny class
Curves	56355b1 56355b2 56355b3 56355b4 56355b5 56355b6 56355b7 56355b8	Curves in isogeny class
deg	122880	Modular degree for the optimal curve
Eigenvalues	-1 3+ 5+  0 -4 13- 17+ -4	Hecke eigenvalues for primes less than 20
L	4.9407467133094	L(r)(E,1)/r!
r	2	Rank of the group of rational points
Twists	195a	Quadratic twists by: 17

Hecke Eigenvalues for isogeny class 56355b

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	-4	-	+	-4	-8	2	8	-6	6	-4	-8	6	-12	2	-4	0	6	-16	-4	10	-18

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Quadratic twists for isogeny class 56355b

17
195a

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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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