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	3450a	Isogeny class
Conductor	3450	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	252685546875000 = 23 · 32 · 516 · 23	Discriminant
Eigenvalues	2+ 3+ 5+  0  2  0 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-19650,-742500]	[a1,a2,a3,a4,a6]
Generators	[-75:600:1]	Generators of the group modulo torsion
j	53706380371489/16171875000	j-invariant
L	2.2404328742487	L(r)(E,1)/r!
Ω	0.41263296025711	Real period
R	2.7148011550661	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	27600cu2 110400cu2 10350bo2 690i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3450a2

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

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Quadratic twists for elliptic curve 3450a2

-4	8	-3	5	-23
27600cu2	110400cu2	10350bo2	690i2	79350c2

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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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