Properties

Label 159120.dt
Number of curves $4$
Conductor $159120$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 159120.dt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159120.dt1 159120dh4 \([0, 0, 0, -294267, -61440694]\) \(1887517194957938/21849165\) \(32620628551680\) \([2]\) \(786432\) \(1.7442\)  
159120.dt2 159120dh2 \([0, 0, 0, -18867, -907774]\) \(994958062276/98903025\) \(73830712550400\) \([2, 2]\) \(393216\) \(1.3976\)  
159120.dt3 159120dh1 \([0, 0, 0, -4287, 92414]\) \(46689225424/7249905\) \(1353006270720\) \([2]\) \(196608\) \(1.0510\) \(\Gamma_0(N)\)-optimal
159120.dt4 159120dh3 \([0, 0, 0, 23253, -4386886]\) \(931329171502/6107473125\) \(-9118408515840000\) \([2]\) \(786432\) \(1.7442\)  

Rank

sage: E.rank()
 

The elliptic curves in class 159120.dt have rank \(1\).

Complex multiplication

The elliptic curves in class 159120.dt do not have complex multiplication.

Modular form 159120.2.a.dt

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4q^{11} - q^{13} - q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.