Cremona's table of elliptic curves

1624 = 2³ · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 7+ 29+	Signs for the Atkin-Lehner involutions
Class	1624a	Isogeny class
Conductor	1624	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	-51968 = -1 · 28 · 7 · 29	Discriminant
Eigenvalues	2+  1  0 7+ -6  4  6 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,7,11]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1]	Generators of the group modulo torsion
j	128000/203	j-invariant
L	3.110079472488	L(r)(E,1)/r!
Ω	2.4215928231777	Real period
R	0.32107787101124	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	3248d1 12992g1 14616k1 40600r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1624a1

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	0	+	-6	4	6	-5	-1	+	8	-8	-7	-10	-5	-11	0	2	9	-15	3	-12	6	11	-1

---

Quadratic twists for elliptic curve 1624a1

-4	8	-3	5	-7	29
3248d1	12992g1	14616k1	40600r1	11368d1	47096h1

---

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