Cremona's table of elliptic curves

522 = 2 · 3² · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 29-	Signs for the Atkin-Lehner involutions
Class	522b	Isogeny class
Conductor	522	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	46503936 = 211 · 33 · 292	Discriminant
Eigenvalues	2+ 3+  2  4  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-32766,2291092]	[a1,a2,a3,a4,a6]
j	144091275020705979/1722368	j-invariant
L	1.4203697589547	L(r)(E,1)/r!
Ω	1.4203697589547	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	4176t2 16704c2 522g2 13050bc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 522b2

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	4	0	2	-2	0	-4	-	6	-4	-2	4	8	14	-6	-8	-12	16	-2	-6	2	-14	-14

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Quadratic twists for elliptic curve 522b2

-4	8	-3	5	-7	-11	13	29
4176t2	16704c2	522g2	13050bc2	25578f2	63162bn2	88218bq2	15138q2

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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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