Cremona's table of elliptic curves

624 = 2⁴ · 3 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+	Signs for the Atkin-Lehner involutions
Class	624a	Isogeny class
Conductor	624	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-8112 = -1 · 24 · 3 · 132	Discriminant
Eigenvalues	2+ 3+  0  0 -6 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3,6]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	-256000/507	j-invariant
L	1.841410874436	L(r)(E,1)/r!
Ω	3.6944854092277	Real period
R	0.99684295400747	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	312a1 2496bc1 1872c1 15600s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624a1

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	0	-6	+	2	0	-4	-6	4	-2	0	-4	-10	-10	6	-6	12	-2	6	16	-6	4	14

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Quadratic twists for elliptic curve 624a1

-4	8	-3	5	-7	-11	13
312a1	2496bc1	1872c1	15600s1	30576ba1	75504d1	8112a1

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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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