Cremona's table of elliptic curves

3450 = 2 · 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 23-	Signs for the Atkin-Lehner involutions
Class	3450r	Isogeny class
Conductor	3450	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	444107667000000 = 26 · 3 · 56 · 236	Discriminant
Eigenvalues	2- 3+ 5+ -2  0 -2  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-19263,167781]	[a1,a2,a3,a4,a6]
Generators	[-135:642:1]	Generators of the group modulo torsion
j	50591419971625/28422890688	j-invariant
L	4.1718218401534	L(r)(E,1)/r!
Ω	0.45618819179705	Real period
R	0.50805322052621	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27600cm4 110400dy4 10350l4 138b4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450r4

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	0	-2	0	2	-	-6	-4	10	-6	-2	0	-12	12	-10	-14	0	-2	-10	0	12	10

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Quadratic twists for elliptic curve 3450r4

-4	8	-3	5	-23
27600cm4	110400dy4	10350l4	138b4	79350cl4

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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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