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	2	Product of Tamagawa factors cp
Δ	1168128 = 28 · 33 · 132	Discriminant
Eigenvalues	2- 3+  0 -2  0 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-148,-644]	[a1,a2,a3,a4,a6]
Generators	[45:286:1]	Generators of the group modulo torsion
j	1409938000/4563	j-invariant
L	1.8217793937192	L(r)(E,1)/r!
Ω	1.3682780803333	Real period
R	2.6628788692946	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	156b2 2496ba2 1872p2 15600ce2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624g2

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 624g2

-4	8	-3	5	-7	-11	13
156b2	2496ba2	1872p2	15600ce2	30576cl2	75504bf2	8112t2

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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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