Cremona's table of elliptic curves

469 = 7 · 67

Field	Data	Notes
Atkin-Lehner	7+ 67+	Signs for the Atkin-Lehner involutions
Class	469a	Isogeny class
Conductor	469	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	1126069 = 75 · 67	Discriminant
Eigenvalues	1  1 -3 7+  0 -1 -8  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-80,-275]	[a1,a2,a3,a4,a6]
Generators	[-5:4:1]	Generators of the group modulo torsion
j	55611739513/1126069	j-invariant
L	2.2667465653699	L(r)(E,1)/r!
Ω	1.6007144150221	Real period
R	1.4160843084171	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	7504t1 30016k1 4221b1 11725c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 469a1

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	-3	+	0	-1	-8	8	3	-3	-1	-3	-9	4	10	6	-14	-6	+	-9	-14	14	10	0	-14

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Quadratic twists for elliptic curve 469a1

-4	8	-3	5	-7	-11	13	-67
7504t1	30016k1	4221b1	11725c1	3283a1	56749e1	79261f1	31423c1

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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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