Cremona's table of elliptic curves

10300 = 2² · 5² · 103

Field	Data	Notes
Atkin-Lehner	2- 5+ 103+	Signs for the Atkin-Lehner involutions
Class	10300a	Isogeny class
Conductor	10300	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2592	Modular degree for the optimal curve
Δ	-128750000 = -1 · 24 · 57 · 103	Discriminant
Eigenvalues	2- -1 5+  0 -4 -2 -8 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-33,562]	[a1,a2,a3,a4,a6]
Generators	[-3:25:1] [1:23:1]	Generators of the group modulo torsion
j	-16384/515	j-invariant
L	5.0857802707469	L(r)(E,1)/r!
Ω	1.5462280134531	Real period
R	0.27409607048559	Regulator
r	2	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	41200bf1 92700h1 2060a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 10300a1

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	+	0	-4	-2	-8	-5	-2	-1	-10	-6	-5	-3	9	9	-7	-13	3	-12	9	5	-12	0	2

---

Quadratic twists for elliptic curve 10300a1

-4	-3	5
41200bf1	92700h1	2060a1

---

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