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	8	Product of Tamagawa factors cp
Δ	892687500 = 22 · 33 · 56 · 232	Discriminant
Eigenvalues	2- 3+ 5+ -2  0 -2  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-14388,658281]	[a1,a2,a3,a4,a6]
Generators	[-75:1187:1]	Generators of the group modulo torsion
j	21081759765625/57132	j-invariant
L	4.1718218401534	L(r)(E,1)/r!
Ω	1.3685645753912	Real period
R	1.5241596615786	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	27600cm2 110400dy2 10350l2 138b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450r2

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 3450r2

-4	8	-3	5	-23
27600cm2	110400dy2	10350l2	138b2	79350cl2

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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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