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	4	Product of Tamagawa factors cp
Δ	29952 = 28 · 32 · 13	Discriminant
Eigenvalues	2+ 3+  0  0 -6 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-68,240]	[a1,a2,a3,a4,a6]
Generators	[4:4:1]	Generators of the group modulo torsion
j	137842000/117	j-invariant
L	1.841410874436	L(r)(E,1)/r!
Ω	3.6944854092277	Real period
R	0.49842147700374	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	312a2 2496bc2 1872c2 15600s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624a2

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 624a2

-4	8	-3	5	-7	-11	13
312a2	2496bc2	1872c2	15600s2	30576ba2	75504d2	8112a2

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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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