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	16	Product of Tamagawa factors cp
Δ	6909765625 = 58 · 72 · 192	Discriminant
Eigenvalues	-1  0 5+ 7- -4  2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-480,-478]	[a1,a2,a3,a4,a6]
Generators	[-20:38:1]	Generators of the group modulo torsion
j	781229961/442225	j-invariant
L	2.0932179216494	L(r)(E,1)/r!
Ω	1.1002541738334	Real period
R	1.9024857814049	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	53200bm2 29925be2 665b2 23275m2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3325g2

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 3325g2

-4	-3	5	-7	-19
53200bm2	29925be2	665b2	23275m2	63175n2

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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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