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
deg	36	Modular degree for the optimal curve
Δ	-469567 = -1 · 73 · 372	Discriminant
Eigenvalues	1  0  4 7-  4  4  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5,-32]	[a1,a2,a3,a4,a6]
j	-15438249/469567	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	4144f1 16576g1 2331g1 6475a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 259a1

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

---

Quadratic twists for elliptic curve 259a1

-4	8	-3	5	-7	-11	13	17	-19	37
4144f1	16576g1	2331g1	6475a1	1813a1	31339c1	43771d1	74851d1	93499k1	9583c1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations