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	624c	Isogeny class
Conductor	624	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-87739392 = -1 · 210 · 3 · 134	Discriminant
Eigenvalues	2+ 3+  2  0  0 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,8,448]	[a1,a2,a3,a4,a6]
j	48668/85683	j-invariant
L	1.49889886741	L(r)(E,1)/r!
Ω	1.49889886741	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	312c4 2496bb4 1872i4 15600m4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624c4

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	0	-	2	4	0	6	0	-2	6	12	4	6	8	-2	-4	12	-14	0	-8	-18	-6

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Quadratic twists for elliptic curve 624c4

-4	8	-3	5	-7	-11	13
312c4	2496bb4	1872i4	15600m4	30576w3	75504a3	8112b4

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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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