Properties

Label 273600.bn
Number of curves $4$
Conductor $273600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 273600.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273600.bn1 273600bn3 \([0, 0, 0, -17761586700, 911106819286000]\) \(207530301091125281552569/805586668007040\) \(2405468901282333327360000000\) \([2]\) \(330301440\) \(4.4672\)  
273600.bn2 273600bn4 \([0, 0, 0, -3366194700, -58041215786000]\) \(1412712966892699019449/330160465517040000\) \(985853867466433167360000000000\) \([2]\) \(330301440\) \(4.4672\)  
273600.bn3 273600bn2 \([0, 0, 0, -1126706700, 13788122326000]\) \(52974743974734147769/3152005008998400\) \(9411836524789078425600000000\) \([2, 2]\) \(165150720\) \(4.1206\)  
273600.bn4 273600bn1 \([0, 0, 0, 52941300, 889851094000]\) \(5495662324535111/117739817533440\) \(-351569211317771304960000000\) \([2]\) \(82575360\) \(3.7740\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 273600.bn have rank \(1\).

Complex multiplication

The elliptic curves in class 273600.bn do not have complex multiplication.

Modular form 273600.2.a.bn

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.