Cremona's table of elliptic curves

464 = 2⁴ · 29

Field	Data	Notes
Atkin-Lehner	2+ 29+	Signs for the Atkin-Lehner involutions
Class	464b	Isogeny class
Conductor	464	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-29696 = -1 · 210 · 29	Discriminant
Eigenvalues	2+ -1  1 -2 -3 -1  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-80,304]	[a1,a2,a3,a4,a6]
Generators	[6:-2:1]	Generators of the group modulo torsion
j	-55990084/29	j-invariant
L	1.6722315624007	L(r)(E,1)/r!
Ω	3.6733647240512	Real period
R	0.22761578117357	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	232b1 1856i1 4176h1 11600a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 464b1

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
+	-1	1	-2	-3	-1	0	0	-4	+	-3	-8	-6	5	-3	5	8	0	12	-6	-4	-1	12	6	14

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Quadratic twists for elliptic curve 464b1

-4	8	-3	5	-7	-11	13	29
232b1	1856i1	4176h1	11600a1	22736f1	56144g1	78416c1	13456a1

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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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