Properties

Label 96600bn
Number of curves $4$
Conductor $96600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 96600bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96600.b4 96600bn1 \([0, -1, 0, -25508, -92988]\) \(458891455696/264449745\) \(1057798980000000\) \([4]\) \(368640\) \(1.5725\) \(\Gamma_0(N)\)-optimal
96600.b2 96600bn2 \([0, -1, 0, -290008, -59869988]\) \(168591300897604/472410225\) \(7558563600000000\) \([2, 2]\) \(737280\) \(1.9191\)  
96600.b3 96600bn3 \([0, -1, 0, -175008, -107939988]\) \(-18524646126002/146738831715\) \(-4695642614880000000\) \([2]\) \(1474560\) \(2.2656\)  
96600.b1 96600bn4 \([0, -1, 0, -4637008, -3841759988]\) \(344577854816148242/2716875\) \(86940000000000\) \([2]\) \(1474560\) \(2.2656\)  

Rank

sage: E.rank()
 

The elliptic curves in class 96600bn have rank \(1\).

Complex multiplication

The elliptic curves in class 96600bn do not have complex multiplication.

Modular form 96600.2.a.bn

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - 4 q^{11} - 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.