Cremona's table of elliptic curves

57798 = 2 · 3² · 13² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+ 19+	Signs for the Atkin-Lehner involutions
Class	57798b	Isogeny class
Conductor	57798	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	489216	Modular degree for the optimal curve
Δ	-263700391698432 = -1 · 213 · 33 · 137 · 19	Discriminant
Eigenvalues	2+ 3+  2  5 -5 13+  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-60111,5741165]	[a1,a2,a3,a4,a6]
Generators	[1094:1481:8]	Generators of the group modulo torsion
j	-184317154371/2023424	j-invariant
L	6.3542650974466	L(r)(E,1)/r!
Ω	0.55418767027368	Real period
R	2.8664771150645	Regulator
r	1	Rank of the group of rational points
S	1.0000000000448	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	57798ba1 4446m1	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 57798b1

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
+	+	2	5	-5	+	4	+	5	-8	-6	8	4	-9	-2	-6	6	-10	-3	-1	-2	5	0	12	-10

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Quadratic twists for elliptic curve 57798b1

-3	13
57798ba1	4446m1

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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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