Properties

Label 145600di
Number of curves $3$
Conductor $145600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("di1")
 
E.isogeny_class()
 

Elliptic curves in class 145600di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
145600.hm2 145600di1 \([0, -1, 0, -733, -7413]\) \(-43614208/91\) \(-91000000\) \([]\) \(62208\) \(0.41278\) \(\Gamma_0(N)\)-optimal
145600.hm3 145600di2 \([0, -1, 0, 1267, -38413]\) \(224755712/753571\) \(-753571000000\) \([]\) \(186624\) \(0.96209\)  
145600.hm1 145600di3 \([0, -1, 0, -11733, 1209587]\) \(-178643795968/524596891\) \(-524596891000000\) \([]\) \(559872\) \(1.5114\)  

Rank

sage: E.rank()
 

The elliptic curves in class 145600di have rank \(0\).

Complex multiplication

The elliptic curves in class 145600di do not have complex multiplication.

Modular form 145600.2.a.di

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.