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	144	Product of Tamagawa factors cp
Δ	-7008192000000 = -1 · 212 · 32 · 56 · 233	Discriminant
Eigenvalues	2- 3+ 5+ -2  0 -2  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,4737,23781]	[a1,a2,a3,a4,a6]
Generators	[91:-1150:1]	Generators of the group modulo torsion
j	752329532375/448524288	j-invariant
L	4.1718218401534	L(r)(E,1)/r!
Ω	0.45618819179705	Real period
R	0.25402661026311	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	27600cm3 110400dy3 10350l3 138b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450r3

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 3450r3

-4	8	-3	5	-23
27600cm3	110400dy3	10350l3	138b3	79350cl3

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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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