Cremona's table of elliptic curves

4092 = 2² · 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 31-	Signs for the Atkin-Lehner involutions
Class	4092d	Isogeny class
Conductor	4092	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-1522224 = -1 · 24 · 32 · 11 · 312	Discriminant
Eigenvalues	2- 3+  2 -2 11- -4  0 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,23,-50]	[a1,a2,a3,a4,a6]
j	80494592/95139	j-invariant
L	1.4407697924883	L(r)(E,1)/r!
Ω	1.4407697924883	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16368u1 65472w1 12276b1 102300x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4092d1

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

---

Quadratic twists for elliptic curve 4092d1

-4	8	-3	5	-11	-31
16368u1	65472w1	12276b1	102300x1	45012d1	126852h1

---

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