Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("348480.qt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 348480qt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
348480.qt4 348480qt1 [0, 0, 0, -197472, 33083336] [2] 3317760 \(\Gamma_0(N)\)-optimal
348480.qt3 348480qt2 [0, 0, 0, -437052, -62844496] [2] 6635520  
348480.qt2 348480qt3 [0, 0, 0, -1939872, -1026818584] [2] 9953280  
348480.qt1 348480qt4 [0, 0, 0, -30929052, -66206090896] [2] 19906560  

Rank

sage: E.rank()
 

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

Modular form 348480.2.a.qt

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

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 Cremona 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 Cremona labels.