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
deg	48	Modular degree for the optimal curve
Δ	151632 = 24 · 36 · 13	Discriminant
Eigenvalues	2- 3+  0 -2  0 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-13,4]	[a1,a2,a3,a4,a6]
Generators	[0:2:1]	Generators of the group modulo torsion
j	16384000/9477	j-invariant
L	1.8217793937192	L(r)(E,1)/r!
Ω	2.7365561606666	Real period
R	1.3314394346473	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	156b1 2496ba1 1872p1 15600ce1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624g1

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 624g1

-4	8	-3	5	-7	-11	13
156b1	2496ba1	1872p1	15600ce1	30576cl1	75504bf1	8112t1

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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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