Properties

Label 99450cr
Number of curves 8
Conductor 99450
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("99450.dq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 99450cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
99450.dq7 99450cr1 [1, -1, 1, -471632855, -3796034014353] [2] 53084160 \(\Gamma_0(N)\)-optimal
99450.dq6 99450cr2 [1, -1, 1, -1250384855, 11970578977647] [2, 2] 106168320  
99450.dq5 99450cr3 [1, -1, 1, -5803376855, 169057784545647] [2] 159252480  
99450.dq8 99450cr4 [1, -1, 1, 3348183145, 79560331441647] [2] 212336640  
99450.dq4 99450cr5 [1, -1, 1, -18308984855, 953434712977647] [2] 212336640  
99450.dq2 99450cr6 [1, -1, 1, -92685938855, 10860999629389647] [2, 2] 318504960  
99450.dq3 99450cr7 [1, -1, 1, -92517868355, 10902350686786647] [2] 637009920  
99450.dq1 99450cr8 [1, -1, 1, -1482975001355, 695102884051264647] [2] 637009920  

Rank

sage: E.rank()
 

The elliptic curves in class 99450cr have rank \(0\).

Modular form 99450.2.a.dq

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 4q^{7} + q^{8} - q^{13} + 4q^{14} + q^{16} + q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.