Cremona's table of elliptic curves

34969 = 11² · 17²

Field	Data	Notes
Atkin-Lehner	11+ 17+	Signs for the Atkin-Lehner involutions
Class	34969a	Isogeny class
Conductor	34969	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	20736	Modular degree for the optimal curve
Δ	-32127104339 = -1 · 113 · 176	Discriminant
Eigenvalues	0  1  3  0 11+  0 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-2119,37824]	[a1,a2,a3,a4,a6]
Generators	[552:-1603:27]	Generators of the group modulo torsion
j	-32768	j-invariant
L	6.8104401863193	L(r)(E,1)/r!
Ω	1.1647582570191	Real period
R	1.4617711755374	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34969a2 121b1	Quadratic twists by: -11 17

Hecke Eigenvalues for elliptic curve 34969a1

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	1	3	0	+	0	+	0	9	0	5	-7	0	0	-12	6	-15	0	13	3	0	0	0	-9	-17

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Quadratic twists for elliptic curve 34969a1

-11	17
34969a2	121b1

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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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