Cremona's table of elliptic curves

13400 = 2³ · 5² · 67

Field	Data	Notes
Atkin-Lehner	2- 5- 67+	Signs for the Atkin-Lehner involutions
Class	13400p	Isogeny class
Conductor	13400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	20160	Modular degree for the optimal curve
Δ	-9398843750000 = -1 · 24 · 59 · 673	Discriminant
Eigenvalues	2-  1 5-  1 -4  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9208,-373787]	[a1,a2,a3,a4,a6]
Generators	[5514:143375:8]	Generators of the group modulo torsion
j	-2763228416/300763	j-invariant
L	5.4122696674555	L(r)(E,1)/r!
Ω	0.24219514158886	Real period
R	5.5866827385034	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	26800o1 107200bj1 120600x1 13400j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13400p1

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	-4	2	0	-4	2	5	6	-4	8	9	-6	-11	3	14	+	8	-14	-2	-2	-3	-1

---

Quadratic twists for elliptic curve 13400p1

-4	8	-3	5
26800o1	107200bj1	120600x1	13400j1

---

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