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	2175c	Isogeny class
Conductor	2175	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	497306953125 = 32 · 57 · 294	Discriminant
Eigenvalues	-1 3+ 5+ -4 -4 -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-6438,-198594]	[a1,a2,a3,a4,a6]
Generators	[-50:62:1] [-44:65:1]	Generators of the group modulo torsion
j	1888690601881/31827645	j-invariant
L	2.0593023447082	L(r)(E,1)/r!
Ω	0.53352569093784	Real period
R	0.48247497254721	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	34800dk4 6525e3 435c3 106575ch4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2175c3

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
-1	+	+	-4	-4	-6	-6	-4	4	-	-8	-2	-6	-4	0	10	-12	-10	-8	-8	2	0	-8	-6	2

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Quadratic twists for elliptic curve 2175c3

-4	-3	5	-7	29
34800dk4	6525e3	435c3	106575ch4	63075o4

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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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