Cremona's table of elliptic curves

1368 = 2³ · 3² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 19+	Signs for the Atkin-Lehner involutions
Class	1368a	Isogeny class
Conductor	1368	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-113689008 = -1 · 24 · 39 · 192	Discriminant
Eigenvalues	2+ 3+ -4  0  6  2 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-162,945]	[a1,a2,a3,a4,a6]
Generators	[4:19:1]	Generators of the group modulo torsion
j	-1492992/361	j-invariant
L	2.3288078838276	L(r)(E,1)/r!
Ω	1.7842835087393	Real period
R	0.65258908475622	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	2736d1 10944i1 1368d1 34200bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1368a1

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

---

Quadratic twists for elliptic curve 1368a1

-4	8	-3	5	-7	-19
2736d1	10944i1	1368d1	34200bt1	67032h1	25992t1

---

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