Properties

Label 207936fl
Number of curves $4$
Conductor $207936$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fl1")
 
E.isogeny_class()
 

Elliptic curves in class 207936fl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
207936.dh3 207936fl1 \([0, 0, 0, -1667820, 63322288]\) \(57066625/32832\) \(295179637510417416192\) \([2]\) \(6635520\) \(2.6174\) \(\Gamma_0(N)\)-optimal
207936.dh4 207936fl2 \([0, 0, 0, 6649620, 505810096]\) \(3616805375/2105352\) \(-18928394255355516813312\) \([2]\) \(13271040\) \(2.9640\)  
207936.dh1 207936fl3 \([0, 0, 0, -89000940, -323174021456]\) \(8671983378625/82308\) \(739998952369865883648\) \([2]\) \(19906560\) \(3.1667\)  
207936.dh2 207936fl4 \([0, 0, 0, -86921580, -338992960592]\) \(-8078253774625/846825858\) \(-7613479221457365143912448\) \([2]\) \(39813120\) \(3.5133\)  

Rank

sage: E.rank()
 

The elliptic curves in class 207936fl have rank \(1\).

Complex multiplication

The elliptic curves in class 207936fl do not have complex multiplication.

Modular form 207936.2.a.fl

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - 4 q^{13} - 6 q^{17} + O(q^{20})\) 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 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.