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	10780f	Isogeny class
Conductor	10780	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	10368	Modular degree for the optimal curve
Δ	28471058000 = 24 · 53 · 76 · 112	Discriminant
Eigenvalues	2-  2 5+ 7- 11+  4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2221,-38730]	[a1,a2,a3,a4,a6]
Generators	[69:363:1]	Generators of the group modulo torsion
j	643956736/15125	j-invariant
L	6.0604274760814	L(r)(E,1)/r!
Ω	0.69641394978912	Real period
R	2.9007783267967	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	43120bw1 97020cv1 53900o1 220a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10780f1

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	4	-6	-6	-8	2	-6	8	-6	-6	12	-2	-10	-12	16	8	0	-6	-14

---

Quadratic twists for elliptic curve 10780f1

-4	-3	5	-7	-11
43120bw1	97020cv1	53900o1	220a1	118580m1

---

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