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Properties

Label 106575.cn
Number of curves $1$
Conductor $106575$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([1, 0, 1, 532114, 117991703]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 106575.cn1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1\)
\(29\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 - T + 2 T^{2}\) 1.2.ab
\(11\) \( 1 + 2 T + 11 T^{2}\) 1.11.c
\(13\) \( 1 + T + 13 T^{2}\) 1.13.b
\(17\) \( 1 - 4 T + 17 T^{2}\) 1.17.ae
\(19\) \( 1 + 7 T + 19 T^{2}\) 1.19.h
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 106575.cn do not have complex multiplication.

Modular form 106575.2.a.cn

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} - 3 q^{8} + q^{9} - 2 q^{11} - q^{12} - q^{13} - q^{16} + 4 q^{17} + q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

Elliptic curves in class 106575.cn

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106575.cn1 106575bt1 \([1, 0, 1, 532114, 117991703]\) \(115615114298495/108606877083\) \(-15652425840373887075\) \([]\) \(1884960\) \(2.3703\) \(\Gamma_0(N)\)-optimal