Properties

Label 348480.qt
Number of curves $4$
Conductor $348480$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("qt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 348480.qt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348480.qt1 348480qt4 \([0, 0, 0, -30929052, -66206090896]\) \(154639330142416/33275\) \(704079407816294400\) \([2]\) \(19906560\) \(2.8093\)  
348480.qt2 348480qt3 \([0, 0, 0, -1939872, -1026818584]\) \(610462990336/8857805\) \(11714121147543598080\) \([2]\) \(9953280\) \(2.4627\)  
348480.qt3 348480qt2 \([0, 0, 0, -437052, -62844496]\) \(436334416/171875\) \(3636773800704000000\) \([2]\) \(6635520\) \(2.2600\)  
348480.qt4 348480qt1 \([0, 0, 0, -197472, 33083336]\) \(643956736/15125\) \(20002255903872000\) \([2]\) \(3317760\) \(1.9134\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 348480.qt have rank \(0\).

Complex multiplication

The elliptic curves in class 348480.qt do not have complex multiplication.

Modular form 348480.2.a.qt

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4q^{7} - 4q^{13} - 4q^{19} + O(q^{20})\)  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.