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	624g	Isogeny class
Conductor	624	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	316368 = 24 · 32 · 133	Discriminant
Eigenvalues	2- 3+  0 -2  0 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-733,7888]	[a1,a2,a3,a4,a6]
Generators	[12:26:1]	Generators of the group modulo torsion
j	2725888000000/19773	j-invariant
L	1.8217793937192	L(r)(E,1)/r!
Ω	2.7365561606666	Real period
R	0.44381314488243	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	156b3 2496ba3 1872p3 15600ce3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624g3

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	-2	0	-	-6	-2	0	-6	-2	2	-12	4	0	6	-12	2	10	-12	14	-8	-12	0	-10

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Quadratic twists for elliptic curve 624g3

-4	8	-3	5	-7	-11	13
156b3	2496ba3	1872p3	15600ce3	30576cl3	75504bf3	8112t3

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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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