Properties

Label 438080do
Number of curves $4$
Conductor $438080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 438080do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
438080.do3 438080do1 \([0, -1, 0, -6573025, -3544299423]\) \(46694890801/18944000\) \(12741540863566413824000\) \([2]\) \(25214976\) \(2.9394\) \(\Gamma_0(N)\)-optimal
438080.do4 438080do2 \([0, -1, 0, 21464095, -25822594975]\) \(1625964918479/1369000000\) \(-920775413968666624000000\) \([2]\) \(50429952\) \(3.2860\)  
438080.do1 438080do3 \([0, -1, 0, -462176225, -3824211706783]\) \(16232905099479601/4052240\) \(2725495225347253207040\) \([2]\) \(75644928\) \(3.4887\)  
438080.do2 438080do4 \([0, -1, 0, -460423905, -3854650556575]\) \(-16048965315233521/256572640900\) \(-172568137061893020870246400\) \([2]\) \(151289856\) \(3.8353\)  

Rank

sage: E.rank()
 

The elliptic curves in class 438080do have rank \(0\).

Complex multiplication

The elliptic curves in class 438080do do not have complex multiplication.

Modular form 438080.2.a.do

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} + 2 q^{7} + q^{9} + 2 q^{13} + 2 q^{15} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.