Properties

Label 39600.bl
Number of curves $3$
Conductor $39600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 39600.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39600.bl1 39600dy3 \([0, 0, 0, -28153200, -57496282000]\) \(-52893159101157376/11\) \(-513216000000\) \([]\) \(840000\) \(2.5439\)  
39600.bl2 39600dy2 \([0, 0, 0, -37200, -5002000]\) \(-122023936/161051\) \(-7513995456000000\) \([]\) \(168000\) \(1.7392\)  
39600.bl3 39600dy1 \([0, 0, 0, -1200, 38000]\) \(-4096/11\) \(-513216000000\) \([]\) \(33600\) \(0.93444\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 39600.bl have rank \(0\).

Complex multiplication

The elliptic curves in class 39600.bl do not have complex multiplication.

Modular form 39600.2.a.bl

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} + q^{11} - 4 q^{13} - 2 q^{17} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.