Properties

Label 348480jf
Number of curves 4
Conductor 348480
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("348480.jf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 348480jf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
348480.jf4 348480jf1 [0, 0, 0, -197472, -33083336] [2] 3317760 \(\Gamma_0(N)\)-optimal
348480.jf3 348480jf2 [0, 0, 0, -437052, 62844496] [2] 6635520  
348480.jf2 348480jf3 [0, 0, 0, -1939872, 1026818584] [2] 9953280  
348480.jf1 348480jf4 [0, 0, 0, -30929052, 66206090896] [2] 19906560  

Rank

sage: E.rank()
 

The elliptic curves in class 348480jf have rank \(1\).

Modular form 348480.2.a.jf

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.