Cremona's table of elliptic curves

17325 = 3² · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	17325w	Isogeny class
Conductor	17325	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	355216640625 = 310 · 57 · 7 · 11	Discriminant
Eigenvalues	1 3- 5+ 7- 11+  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-462042,120999991]	[a1,a2,a3,a4,a6]
Generators	[3342:5279:8]	Generators of the group modulo torsion
j	957681397954009/31185	j-invariant
L	5.824234021941	L(r)(E,1)/r!
Ω	0.70376495465621	Real period
R	4.1379113746763	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	5775i3 3465n4 121275df4	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 17325w4

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	-	+	-	+	2	-2	-4	-4	6	-4	2	6	4	8	2	12	-2	4	-16	-2	-4	0	-6	-14

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Quadratic twists for elliptic curve 17325w4

-3	5	-7
5775i3	3465n4	121275df4

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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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