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	1407d	Isogeny class
Conductor	1407	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-265923 = -1 · 34 · 72 · 67	Discriminant
Eigenvalues	0 3- -2 7-  0  0  1 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-29,56]	[a1,a2,a3,a4,a6]
Generators	[-2:10:1]	Generators of the group modulo torsion
j	-2791309312/265923	j-invariant
L	2.543003496639	L(r)(E,1)/r!
Ω	3.0284331246017	Real period
R	0.10496366404712	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	22512m1 90048o1 4221f1 35175b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1407d1

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
0	-	-2	-	0	0	1	-3	5	-5	-10	-1	-12	-8	1	6	3	-12	+	-8	11	-14	-4	1	-8

---

Quadratic twists for elliptic curve 1407d1

-4	8	-3	5	-7	-67
22512m1	90048o1	4221f1	35175b1	9849c1	94269a1

---

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