Cremona's table of elliptic curves

3325 = 5² · 7 · 19

Field	Data	Notes
Atkin-Lehner	5- 7- 19-	Signs for the Atkin-Lehner involutions
Class	3325k	Isogeny class
Conductor	3325	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	29760	Modular degree for the optimal curve
Δ	-87304888671875 = -1 · 59 · 73 · 194	Discriminant
Eigenvalues	2  3 5- 7-  5 -5  1 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,9125,-299219]	[a1,a2,a3,a4,a6]
j	43022168064/44700103	j-invariant
L	7.8762511496325	L(r)(E,1)/r!
Ω	0.32817713123469	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53200dj1 29925bn1 3325h1 23275bb1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3325k1

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	3	-	-	5	-5	1	-	6	-9	2	2	2	8	3	-14	6	-4	-10	-8	10	-17	12	4	-3

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Quadratic twists for elliptic curve 3325k1

-4	-3	5	-7	-19
53200dj1	29925bn1	3325h1	23275bb1	63175z1

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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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