Cremona's table of elliptic curves

12410 = 2 · 5 · 17 · 73

Field	Data	Notes
Atkin-Lehner	2- 5+ 17- 73-	Signs for the Atkin-Lehner involutions
Class	12410n	Isogeny class
Conductor	12410	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	10240	Modular degree for the optimal curve
Δ	2033254400 = 216 · 52 · 17 · 73	Discriminant
Eigenvalues	2- -2 5+ -4  0 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-561,4585]	[a1,a2,a3,a4,a6]
Generators	[-26:55:1] [-22:91:1]	Generators of the group modulo torsion
j	19528130963089/2033254400	j-invariant
L	6.0310568482949	L(r)(E,1)/r!
Ω	1.4282285521331	Real period
R	0.52784416395478	Regulator
r	2	Rank of the group of rational points
S	0.99999999999979	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	99280r1 111690t1 62050a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12410n1

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	+	-4	0	-6	-	-4	2	-2	-8	2	-6	-6	-2	-6	-14	-14	-12	-10	-	-2	6	-10	-6

---

Quadratic twists for elliptic curve 12410n1

-4	-3	5
99280r1	111690t1	62050a1

---

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