Cremona's table of elliptic curves

45486 = 2 · 3² · 7 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 19-	Signs for the Atkin-Lehner involutions
Class	45486k	Isogeny class
Conductor	45486	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	460800	Modular degree for the optimal curve
Δ	31035952601932068 = 22 · 311 · 72 · 197	Discriminant
Eigenvalues	2+ 3-  2 7+  2 -2  4 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-297351,61905865]	[a1,a2,a3,a4,a6]
Generators	[-432:10685:1]	Generators of the group modulo torsion
j	84778086457/904932	j-invariant
L	5.0794971912746	L(r)(E,1)/r!
Ω	0.37247457374919	Real period
R	3.4092912303665	Regulator
r	1	Rank of the group of rational points
S	1.0000000000008	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15162s1 2394l1	Quadratic twists by: -3 -19

Hecke Eigenvalues for elliptic curve 45486k1

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

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Quadratic twists for elliptic curve 45486k1

-3	-19
15162s1	2394l1

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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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