Cremona's table of elliptic curves

3445 = 5 · 13 · 53

Field	Data	Notes
Atkin-Lehner	5+ 13+ 53+	Signs for the Atkin-Lehner involutions
Class	3445a	Isogeny class
Conductor	3445	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-296700625 = -1 · 54 · 132 · 532	Discriminant
Eigenvalues	1 -2 5+ -2  2 13+  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-354,-2719]	[a1,a2,a3,a4,a6]
Generators	[25:52:1]	Generators of the group modulo torsion
j	-4886171981209/296700625	j-invariant
L	2.5263941848841	L(r)(E,1)/r!
Ω	0.5485813612124	Real period
R	2.3026613402437	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	55120f2 31005o2 17225f2 44785g2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3445a2

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

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Quadratic twists for elliptic curve 3445a2

-4	-3	5	13
55120f2	31005o2	17225f2	44785g2

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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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