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	3450u	Isogeny class
Conductor	3450	Conductor
∏ cp	168	Product of Tamagawa factors cp
Δ	343775896875000 = 23 · 314 · 58 · 23	Discriminant
Eigenvalues	2- 3- 5+ -4 -2  0 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-18838,-442708]	[a1,a2,a3,a4,a6]
Generators	[-58:704:1]	Generators of the group modulo torsion
j	47316161414809/22001657400	j-invariant
L	5.3415625736468	L(r)(E,1)/r!
Ω	0.42617925544217	Real period
R	0.29841917374733	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	27600bu2 110400r2 10350t2 690b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450u2

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

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Quadratic twists for elliptic curve 3450u2

-4	8	-3	5	-23
27600bu2	110400r2	10350t2	690b2	79350dk2

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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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