Cremona's table of elliptic curves

6845 = 5 · 37²

Field	Data	Notes
Atkin-Lehner	5+ 37-	Signs for the Atkin-Lehner involutions
Class	6845b	Isogeny class
Conductor	6845	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	74592	Modular degree for the optimal curve
Δ	2030652184298078125 = 56 · 379	Discriminant
Eigenvalues	0 -1 5+  1  3  0  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-472761,104815596]	[a1,a2,a3,a4,a6]
j	89915392/15625	j-invariant
L	0.99824923077173	L(r)(E,1)/r!
Ω	0.24956230769293	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	109520q1 61605m1 34225i1 6845e1	Quadratic twists by: -4 -3 5 37

Hecke Eigenvalues for elliptic curve 6845b1

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
0	-1	+	1	3	0	6	-6	6	6	-6	-	3	6	-3	-9	-12	-6	-4	9	-7	-12	15	0	6

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Quadratic twists for elliptic curve 6845b1

-4	-3	5	37
109520q1	61605m1	34225i1	6845e1

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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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