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	2175g	Isogeny class
Conductor	2175	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-45981675 = -1 · 37 · 52 · 292	Discriminant
Eigenvalues	0 3- 5+ -1 -2  3 -4  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-153,749]	[a1,a2,a3,a4,a6]
Generators	[27:130:1]	Generators of the group modulo torsion
j	-15947530240/1839267	j-invariant
L	3.0011679037068	L(r)(E,1)/r!
Ω	1.9625494042399	Real period
R	0.10922993098463	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	34800by1 6525c1 2175d1 106575m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2175g1

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	-	+	-1	-2	3	-4	1	0	-	-1	-6	-8	1	-6	2	0	-3	-5	-6	6	-12	-6	-4	1

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Quadratic twists for elliptic curve 2175g1

-4	-3	5	-7	29
34800by1	6525c1	2175d1	106575m1	63075a1

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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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