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
deg	2880	Modular degree for the optimal curve
Δ	-5038727352687 = -1 · 36 · 73 · 674	Discriminant
Eigenvalues	-1 3-  2 7+ -4  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,3713,-63568]	[a1,a2,a3,a4,a6]
Generators	[41:377:1]	Generators of the group modulo torsion
j	5660975162375567/5038727352687	j-invariant
L	2.2342596264526	L(r)(E,1)/r!
Ω	0.42166858851738	Real period
R	3.5324101870435	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	22512o1 90048c1 4221d1 35175h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1407c1

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 1407c1

-4	8	-3	5	-7	-67
22512o1	90048c1	4221d1	35175h1	9849j1	94269g1

---

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