Cremona's table of elliptic curves

4624 = 2⁴ · 17²

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	4624d	Isogeny class
Conductor	4624	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	105046700288 = 28 · 177	Discriminant
Eigenvalues	2+ -2  2 -2 -6  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1252,-7332]	[a1,a2,a3,a4,a6]
Generators	[147:1734:1]	Generators of the group modulo torsion
j	35152/17	j-invariant
L	2.637821161592	L(r)(E,1)/r!
Ω	0.84234161774381	Real period
R	1.5657668492371	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	2312c1 18496p1 41616y1 115600g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4624d1

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

---

Quadratic twists for elliptic curve 4624d1

-4	8	-3	5	17
2312c1	18496p1	41616y1	115600g1	272c1

---

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