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	3450o	Isogeny class
Conductor	3450	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	5312606484375000 = 23 · 35 · 510 · 234	Discriminant
Eigenvalues	2- 3+ 5+  0 -4  6  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-266088,52603281]	[a1,a2,a3,a4,a6]
j	133345896593725369/340006815000	j-invariant
L	2.5853288392572	L(r)(E,1)/r!
Ω	0.43088813987619	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27600cv4 110400cv4 10350o3 690e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450o3

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	-4	6	6	4	+	-6	-8	-6	10	-4	8	14	0	10	-4	8	-2	-12	16	-2	14

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Quadratic twists for elliptic curve 3450o3

-4	8	-3	5	-23
27600cv4	110400cv4	10350o3	690e3	79350cc4

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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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