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	3325a	Isogeny class
Conductor	3325	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	1200	Modular degree for the optimal curve
Δ	1298828125 = 510 · 7 · 19	Discriminant
Eigenvalues	1  1 5+ 7+  3  1  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-326,1423]	[a1,a2,a3,a4,a6]
Generators	[-17:54:1]	Generators of the group modulo torsion
j	390625/133	j-invariant
L	4.6839978949036	L(r)(E,1)/r!
Ω	1.4056779225585	Real period
R	3.3321985212503	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	53200cu1 29925q1 3325i1 23275u1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3325a1

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	1	+	+	3	1	6	+	-8	-2	-5	6	-1	-7	-10	-2	-11	-10	-6	8	0	0	-2	-1	1

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Quadratic twists for elliptic curve 3325a1

-4	-3	5	-7	-19
53200cu1	29925q1	3325i1	23275u1	63175h1

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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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