Cremona's table of elliptic curves

462 = 2 · 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	462a	Isogeny class
Conductor	462	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-274428 = -1 · 22 · 34 · 7 · 112	Discriminant
Eigenvalues	2+ 3+  0 7+ 11+ -2 -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,5,-23]	[a1,a2,a3,a4,a6]
Generators	[4:7:1]	Generators of the group modulo torsion
j	9938375/274428	j-invariant
L	1.2866215632196	L(r)(E,1)/r!
Ω	1.4946342423323	Real period
R	0.43041351749438	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	3696ba1 14784z1 1386i1 11550ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 462a1

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

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Quadratic twists for elliptic curve 462a1

-4	8	-3	5	-7	-11	13
3696ba1	14784z1	1386i1	11550ck1	3234k1	5082t1	78078co1

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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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