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	336	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-5784615000000 = -1 · 26 · 37 · 57 · 232	Discriminant
Eigenvalues	2- 3- 5+ -4 -2  0 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,4162,-51708]	[a1,a2,a3,a4,a6]
Generators	[22:214:1]	Generators of the group modulo torsion
j	510273943271/370215360	j-invariant
L	5.3415625736468	L(r)(E,1)/r!
Ω	0.42617925544217	Real period
R	0.14920958687367	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	27600bu1 110400r1 10350t1 690b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450u1

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 3450u1

-4	8	-3	5	-23
27600bu1	110400r1	10350t1	690b1	79350dk1

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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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