Cremona's table of elliptic curves

5612 = 2² · 23 · 61

Field	Data	Notes
Atkin-Lehner	2- 23- 61-	Signs for the Atkin-Lehner involutions
Class	5612a	Isogeny class
Conductor	5612	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-724374512 = -1 · 24 · 233 · 612	Discriminant
Eigenvalues	2- -3  0  0 -4 -5 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-685,7021]	[a1,a2,a3,a4,a6]
Generators	[-11:115:1] [5:61:1]	Generators of the group modulo torsion
j	-2221648992000/45273407	j-invariant
L	3.3223493496724	L(r)(E,1)/r!
Ω	1.604500253745	Real period
R	0.11503579599935	Regulator
r	2	Rank of the group of rational points
S	0.99999999999986	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	22448d1 89792e1 50508a1 129076b1	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 5612a1

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
-	-3	0	0	-4	-5	-8	-4	-	-5	3	-8	3	2	-7	2	0	-	4	-9	5	-14	6	-14	12

---

Quadratic twists for elliptic curve 5612a1

-4	8	-3	-23
22448d1	89792e1	50508a1	129076b1

---

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