Cremona's table of elliptic curves

115434 = 2 · 3² · 11² · 53

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 53-	Signs for the Atkin-Lehner involutions
Class	115434m	Isogeny class
Conductor	115434	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	1064448	Modular degree for the optimal curve
Δ	-55145849114828736 = -1 · 26 · 33 · 118 · 533	Discriminant
Eigenvalues	2+ 3+ -3 -1 11-  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-130521,21411693]	[a1,a2,a3,a4,a6]
Generators	[-393:3645:1]	Generators of the group modulo torsion
j	-42487533099/9528128	j-invariant
L	3.6354456388867	L(r)(E,1)/r!
Ω	0.33775421220559	Real period
R	2.6908958523628	Regulator
r	1	Rank of the group of rational points
S	1.0000000010778	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	115434bg2 115434bm1	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 115434m1

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
+	+	-3	-1	-	2	6	2	-3	6	-4	-7	-3	-1	-6	-	0	8	2	9	-4	8	3	-12	2

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Quadratic twists for elliptic curve 115434m1

-3	-11
115434bg2	115434bm1

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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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