Cremona's table of elliptic curves

4550 = 2 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	4550a	Isogeny class
Conductor	4550	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7296	Modular degree for the optimal curve
Δ	-5318495436800 = -1 · 219 · 52 · 74 · 132	Discriminant
Eigenvalues	2+  1 5+ 7+  1 13+  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2796,124458]	[a1,a2,a3,a4,a6]
Generators	[48:294:1]	Generators of the group modulo torsion
j	-96643333791265/212739817472	j-invariant
L	3.1199847587875	L(r)(E,1)/r!
Ω	0.67828513051126	Real period
R	1.1499532491726	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36400bt1 40950dn1 4550z1 31850w1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4550a1

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	+	+	1	+	3	1	4	-8	-6	4	3	4	0	-10	-12	0	-7	12	11	-8	9	-3	-6

---

Quadratic twists for elliptic curve 4550a1

-4	-3	5	-7	13
36400bt1	40950dn1	4550z1	31850w1	59150bs1

---

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