Cremona's table of elliptic curves

4624 = 2⁴ · 17²

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	4624c	Isogeny class
Conductor	4624	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	1257728 = 28 · 173	Discriminant
Eigenvalues	2+ -2  0  2  2 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-28,12]	[a1,a2,a3,a4,a6]
Generators	[-2:8:1]	Generators of the group modulo torsion
j	2000	j-invariant
L	2.8103849595659	L(r)(E,1)/r!
Ω	2.4125268527471	Real period
R	1.1649134418404	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	2312a1 18496m1 41616s1 115600h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4624c1

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	0	2	2	-2	+	4	-6	-8	6	8	0	-12	8	-6	4	-8	-4	6	8	2	-4	-14	8

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Quadratic twists for elliptic curve 4624c1

-4	8	-3	5	17
2312a1	18496m1	41616s1	115600h1	4624b1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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