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	3325g	Isogeny class
Conductor	3325	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	71269296875 = 57 · 7 · 194	Discriminant
Eigenvalues	-1  0 5+ 7- -4  2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-4855,130772]	[a1,a2,a3,a4,a6]
Generators	[-76:275:1]	Generators of the group modulo torsion
j	809818183161/4561235	j-invariant
L	2.0932179216494	L(r)(E,1)/r!
Ω	1.1002541738334	Real period
R	0.95124289070247	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	53200bm4 29925be4 665b3 23275m4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3325g3

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

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Quadratic twists for elliptic curve 3325g3

-4	-3	5	-7	-19
53200bm4	29925be4	665b3	23275m4	63175n4

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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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