Properties

Label 272832.fb
Number of curves $6$
Conductor $272832$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fb1")
 
E.isogeny_class()
 

Elliptic curves in class 272832.fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272832.fb1 272832fb3 \([0, 1, 0, -641700929, 6256511805375]\) \(947531277805646290177/38367\) \(1183275858788352\) \([2]\) \(37748736\) \(3.3033\)  
272832.fb2 272832fb6 \([0, 1, 0, -133182849, -480959045505]\) \(8471112631466271697/1662662681263647\) \(51278145595110013246636032\) \([2]\) \(75497472\) \(3.6499\)  
272832.fb3 272832fb4 \([0, 1, 0, -40874689, 93806943551]\) \(244883173420511137/18418027974129\) \(568030022370145788493824\) \([2, 2]\) \(37748736\) \(3.3033\)  
272832.fb4 272832fb2 \([0, 1, 0, -40106369, 97747656831]\) \(231331938231569617/1472026689\) \(45398744874132701184\) \([2, 2]\) \(18874368\) \(2.9568\)  
272832.fb5 272832fb1 \([0, 1, 0, -2458689, 1587952575]\) \(-53297461115137/4513839183\) \(-139211221510590824448\) \([2]\) \(9437184\) \(2.6102\) \(\Gamma_0(N)\)-optimal
272832.fb6 272832fb5 \([0, 1, 0, 39140351, 416379575807]\) \(215015459663151503/2552757445339983\) \(-78729539927881458638389248\) \([2]\) \(75497472\) \(3.6499\)  

Rank

sage: E.rank()
 

The elliptic curves in class 272832.fb have rank \(0\).

Complex multiplication

The elliptic curves in class 272832.fb do not have complex multiplication.

Modular form 272832.2.a.fb

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{9} + 4 q^{11} - 2 q^{13} - 2 q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.