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Properties

Label 106575.cu
Number of curves $1$
Conductor $106575$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([0, -1, 1, 292, 8693]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 106575.cu1 has rank \(0\).

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 \(\mathbb{F}_p\)
\(2\) \( 1 - 2 T + 2 T^{2}\) 1.2.ac
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(13\) \( 1 + 13 T^{2}\) 1.13.a
\(17\) \( 1 - 3 T + 17 T^{2}\) 1.17.ad
\(19\) \( 1 + 3 T + 19 T^{2}\) 1.19.d
\(23\) \( 1 - 9 T + 23 T^{2}\) 1.23.aj
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 106575.2.a.cu

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

Isogeny graph

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

Elliptic curves in class 106575.cu

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106575.cu1 106575bm1 \([0, -1, 1, 292, 8693]\) \(20480/261\) \(-34969921875\) \([]\) \(122880\) \(0.70397\) \(\Gamma_0(N)\)-optimal