Cremona's table of elliptic curves

522 = 2 · 3² · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 29+	Signs for the Atkin-Lehner involutions
Class	522a	Isogeny class
Conductor	522	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-18265824 = -1 · 25 · 39 · 29	Discriminant
Eigenvalues	2+ 3+  3 -5 -4 -6 -1 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,12,-208]	[a1,a2,a3,a4,a6]
Generators	[7:10:1]	Generators of the group modulo torsion
j	9261/928	j-invariant
L	1.5670842850316	L(r)(E,1)/r!
Ω	1.0344899409754	Real period
R	0.75741881238304	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4176q1 16704m1 522i1 13050z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 522a1

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
+	+	3	-5	-4	-6	-1	-5	6	+	0	1	7	1	-13	-2	-13	-2	-4	10	-12	8	12	6	-12

---

Quadratic twists for elliptic curve 522a1

-4	8	-3	5	-7	-11	13	29
4176q1	16704m1	522i1	13050z1	25578d1	63162bq1	88218bl1	15138r1

---

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