Cremona's table of elliptic curves

12320 = 2⁵ · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	12320f	Isogeny class
Conductor	12320	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-3968296640 = -1 · 26 · 5 · 7 · 116	Discriminant
Eigenvalues	2-  0 5- 7+ 11+ -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-397,-4296]	[a1,a2,a3,a4,a6]
Generators	[34760:271731:512]	Generators of the group modulo torsion
j	-108122295744/62004635	j-invariant
L	4.4512627326459	L(r)(E,1)/r!
Ω	0.52098589580906	Real period
R	8.5439217615159	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12320l1 24640bf2 110880bd1 61600j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320f1

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

---

Quadratic twists for elliptic curve 12320f1

-4	8	-3	5	-7
12320l1	24640bf2	110880bd1	61600j1	86240u1

---

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