Cremona's table of elliptic curves

259 = 7 · 37

Field	Data	Notes
Atkin-Lehner	7- 37+	Signs for the Atkin-Lehner involutions
Class	259a	Isogeny class
Conductor	259	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	4353013 = 76 · 37	Discriminant
Eigenvalues	1  0  4 7-  4  4  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-190,-957]	[a1,a2,a3,a4,a6]
j	760798453689/4353013	j-invariant
L	1.9290565396937	L(r)(E,1)/r!
Ω	1.2860376931291	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4144f2 16576g2 2331g2 6475a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 259a2

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	-	4	4	0	-6	-4	-6	2	+	-6	-4	-12	10	-10	-8	-4	0	2	4	0	16	4

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Quadratic twists for elliptic curve 259a2

-4	8	-3	5	-7	-11	13	17	-19	37
4144f2	16576g2	2331g2	6475a2	1813a2	31339c2	43771d2	74851d2	93499k2	9583c2

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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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