Cremona's table of elliptic curves

4056 = 2³ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+	Signs for the Atkin-Lehner involutions
Class	4056d	Isogeny class
Conductor	4056	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	10018961335620432 = 24 · 310 · 139	Discriminant
Eigenvalues	2+ 3+ -4  0  2 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-110075,13242696]	[a1,a2,a3,a4,a6]
Generators	[-17:3887:1]	Generators of the group modulo torsion
j	1909913257984/129730653	j-invariant
L	2.3326806541239	L(r)(E,1)/r!
Ω	0.399843111457	Real period
R	2.9169949253643	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	8112q1 32448bp1 12168t1 101400cw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056d1

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

---

Quadratic twists for elliptic curve 4056d1

-4	8	-3	5	13
8112q1	32448bp1	12168t1	101400cw1	312e1

---

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