Cremona's table of elliptic curves

3538 = 2 · 29 · 61

Field	Data	Notes
Atkin-Lehner	2- 29+ 61+	Signs for the Atkin-Lehner involutions
Class	3538d	Isogeny class
Conductor	3538	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-2568629578576 = -1 · 24 · 294 · 613	Discriminant
Eigenvalues	2-  2  1  1  3  5 -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1340,78829]	[a1,a2,a3,a4,a6]
j	-266108264948161/2568629578576	j-invariant
L	5.5431476519152	L(r)(E,1)/r!
Ω	0.6928934564894	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	28304c1 113216h1 31842l1 88450a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3538d1

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	1	1	3	5	-4	0	7	+	0	8	-7	-8	-8	10	-3	+	-3	8	1	15	4	-4	-14

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Quadratic twists for elliptic curve 3538d1

-4	8	-3	5	29
28304c1	113216h1	31842l1	88450a1	102602b1

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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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