Cremona's table of elliptic curves

441 = 3² · 7²

Field	Data	Notes
Atkin-Lehner	3+ 7+	Signs for the Atkin-Lehner involutions
Class	441b	Isogeny class
Conductor	441	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-64827 = -1 · 33 · 74	Discriminant
Eigenvalues	0 3+  0 7+  0 -7  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,0,12]	[a1,a2,a3,a4,a6]
Generators	[2:4:1]	Generators of the group modulo torsion
j	0	j-invariant
L	1.6517711258984	L(r)(E,1)/r!
Ω	2.7705733999146	Real period
R	0.89427578021359	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	7056bc1 28224b1 441b2 11025b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 441b1

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	+	0	+	0	-7	0	-7	0	0	-7	-1	0	5	0	0	0	14	11	0	-7	-13	0	0	14

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Quadratic twists for elliptic curve 441b1

-4	8	-3	5	-7	-11	13	17
7056bc1	28224b1	441b2	11025b1	441a1	53361c1	74529c1	127449c1

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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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