Properties

Label 145200.hf
Number of curves $4$
Conductor $145200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 145200.hf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145200.hf1 145200br4 \([0, 1, 0, -756238908, -8004796890312]\) \(6749703004355978704/5671875\) \(40192290187500000000\) \([2]\) \(19906560\) \(3.4972\)  
145200.hf2 145200br3 \([0, 1, 0, -47254533, -125144546562]\) \(-26348629355659264/24169921875\) \(-10704622741699218750000\) \([2]\) \(9953280\) \(3.1506\)  
145200.hf3 145200br2 \([0, 1, 0, -9547908, -10459506312]\) \(13584145739344/1195803675\) \(8473756617146700000000\) \([2]\) \(6635520\) \(2.9479\)  
145200.hf4 145200br1 \([0, 1, 0, 661467, -760600062]\) \(72268906496/606436875\) \(-268584979177968750000\) \([2]\) \(3317760\) \(2.6013\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 145200.hf have rank \(0\).

Complex multiplication

The elliptic curves in class 145200.hf do not have complex multiplication.

Modular form 145200.2.a.hf

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{7} + q^{9} + 2q^{13} + 2q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.