Cremona's table of elliptic curves

61605 = 3² · 5 · 37²

Field	Data	Notes
Atkin-Lehner	3- 5- 37+	Signs for the Atkin-Lehner involutions
Conductor	61605	Conductor
Count	8	Number of curves in isogeny class
Curves	61605k1 61605k2 61605k3 61605k4 61605k5 61605k6 61605k7 61605k8	Curves in isogeny class
deg	96768	Modular degree for the optimal curve
Eigenvalues	-1 3- 5-  0  4  2  2 -4	Hecke eigenvalues for primes less than 20
L	4.5313316613739	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	20535a 45a	Quadratic twists by: -3 37

Hecke Eigenvalues for isogeny class 61605k

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

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Quadratic twists for isogeny class 61605k

-3	37
20535a	45a

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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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