Cremona's table of elliptic curves

1407 = 3 · 7 · 67

Field	Data	Notes
Atkin-Lehner	3- 7+ 67-	Signs for the Atkin-Lehner involutions
Class	1407c	Isogeny class
Conductor	1407	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	6490513177869861 = 324 · 73 · 67	Discriminant
Eigenvalues	-1 3-  2 7+ -4  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-133637,18388500]	[a1,a2,a3,a4,a6]
Generators	[-311:5623:1]	Generators of the group modulo torsion
j	263939304644887918033/6490513177869861	j-invariant
L	2.2342596264526	L(r)(E,1)/r!
Ω	0.42166858851738	Real period
R	0.88310254676086	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	22512o3 90048c3 4221d3 35175h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1407c4

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	-	2	+	-4	2	-6	-8	0	-2	8	-10	6	4	-4	-2	0	-14	-	0	2	-8	16	-14	-18

---

Quadratic twists for elliptic curve 1407c4

-4	8	-3	5	-7	-67
22512o3	90048c3	4221d3	35175h3	9849j3	94269g3

---

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