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	624b	Isogeny class
Conductor	624	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2426112 = 28 · 36 · 13	Discriminant
Eigenvalues	2+ 3+ -4  4  2 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-60,-144]	[a1,a2,a3,a4,a6]
Generators	[-4:4:1]	Generators of the group modulo torsion
j	94875856/9477	j-invariant
L	1.713163480429	L(r)(E,1)/r!
Ω	1.7240319881874	Real period
R	0.99369587813171	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	312f2 2496bd2 1872f2 15600u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624b2

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
+	+	-4	4	2	+	-6	-4	-4	-6	-8	-10	-4	4	6	6	6	-6	0	-10	-2	0	10	8	-10

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Quadratic twists for elliptic curve 624b2

-4	8	-3	5	-7	-11	13
312f2	2496bd2	1872f2	15600u2	30576bg2	75504i2	8112e2

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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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