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	2175d	Isogeny class
Conductor	2175	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	-718463671875 = -1 · 37 · 58 · 292	Discriminant
Eigenvalues	0 3+ 5-  1 -2 -3  4  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-3833,101318]	[a1,a2,a3,a4,a6]
Generators	[-8:362:1]	Generators of the group modulo torsion
j	-15947530240/1839267	j-invariant
L	2.2341427407567	L(r)(E,1)/r!
Ω	0.87767877541645	Real period
R	0.42425216820672	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	34800dq1 6525i1 2175g1 106575cx1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2175d1

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 2175d1

-4	-3	5	-7	29
34800dq1	6525i1	2175g1	106575cx1	63075s1

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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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