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	624b	Isogeny class
Conductor	624	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-73008 = -1 · 24 · 33 · 132	Discriminant
Eigenvalues	2+ 3+ -4  4  2 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,5,-14]	[a1,a2,a3,a4,a6]
Generators	[6:14:1]	Generators of the group modulo torsion
j	702464/4563	j-invariant
L	1.713163480429	L(r)(E,1)/r!
Ω	1.7240319881874	Real period
R	1.9873917562634	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	312f1 2496bd1 1872f1 15600u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624b1

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

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Quadratic twists for elliptic curve 624b1

-4	8	-3	5	-7	-11	13
312f1	2496bd1	1872f1	15600u1	30576bg1	75504i1	8112e1

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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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