Cremona's table of elliptic curves

2175 = 3 · 5² · 29

Field	Data	Notes
Atkin-Lehner	3+ 5- 29-	Signs for the Atkin-Lehner involutions
Class	2175f	Isogeny class
Conductor	2175	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4560	Modular degree for the optimal curve
Δ	-169921875 = -1 · 3 · 59 · 29	Discriminant
Eigenvalues	2 3+ 5-  2 -3 -4 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-17458,-882057]	[a1,a2,a3,a4,a6]
Generators	[96803706:659971191:551368]	Generators of the group modulo torsion
j	-301302001664/87	j-invariant
L	4.9536261677107	L(r)(E,1)/r!
Ω	0.20766765372556	Real period
R	11.926812093368	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34800dt1 6525m1 2175j1 106575dc1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2175f1

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	+	-	2	-3	-4	-8	0	1	-	-8	7	7	-9	12	-9	10	2	-8	-8	1	-10	-9	10	-13

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Quadratic twists for elliptic curve 2175f1

-4	-3	5	-7	29
34800dt1	6525m1	2175j1	106575dc1	63075u1

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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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