Cremona's table of elliptic curves

10780 = 2² · 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	10780k	Isogeny class
Conductor	10780	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	24192	Modular degree for the optimal curve
Δ	-22321309472000 = -1 · 28 · 53 · 78 · 112	Discriminant
Eigenvalues	2-  1 5- 7+ 11+ -4  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,6060,138788]	[a1,a2,a3,a4,a6]
Generators	[136:1870:1]	Generators of the group modulo torsion
j	16674224/15125	j-invariant
L	5.4394888464676	L(r)(E,1)/r!
Ω	0.44263868380584	Real period
R	2.0481297897789	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	43120cg1 97020bf1 53900b1 10780e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10780k1

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	-	+	+	-4	6	2	-9	9	-4	2	3	11	-12	0	0	-7	5	-6	2	-16	9	9	-4

---

Quadratic twists for elliptic curve 10780k1

-4	-3	5	-7	-11
43120cg1	97020bf1	53900b1	10780e1	118580q1

---

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