Cremona's table of elliptic curves

1624 = 2³ · 7 · 29

Field	Data	Notes
Atkin-Lehner	2+ 7- 29+	Signs for the Atkin-Lehner involutions
Class	1624b	Isogeny class
Conductor	1624	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-248419720192 = -1 · 210 · 73 · 294	Discriminant
Eigenvalues	2+  2  0 7-  0  4  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2128,45468]	[a1,a2,a3,a4,a6]
j	-1041220466500/242597383	j-invariant
L	2.8233683519149	L(r)(E,1)/r!
Ω	0.94112278397164	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	3248b1 12992t1 14616o1 40600m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1624b1

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	4	2	6	0	+	0	2	10	-8	8	6	10	-12	-12	8	14	0	2	-10	-14

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Quadratic twists for elliptic curve 1624b1

-4	8	-3	5	-7	29
3248b1	12992t1	14616o1	40600m1	11368g1	47096k1

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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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