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	2	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	16848 = 24 · 34 · 13	Discriminant
Eigenvalues	2+ 3+  2  0  0 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7,-2]	[a1,a2,a3,a4,a6]
j	2725888/1053	j-invariant
L	1.49889886741	L(r)(E,1)/r!
Ω	2.9977977348199	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	312c1 2496bb1 1872i1 15600m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 624c1

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 624c1

-4	8	-3	5	-7	-11	13
312c1	2496bb1	1872i1	15600m1	30576w1	75504a1	8112b1

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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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