Properties

Label 96600.bd
Number of curves $2$
Conductor $96600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 96600.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96600.bd1 96600bt1 \([0, -1, 0, -2408, -37188]\) \(96550276/16905\) \(270480000000\) \([2]\) \(104448\) \(0.91345\) \(\Gamma_0(N)\)-optimal
96600.bd2 96600bt2 \([0, -1, 0, 4592, -219188]\) \(334568302/833175\) \(-26661600000000\) \([2]\) \(208896\) \(1.2600\)  

Rank

sage: E.rank()
 

The elliptic curves in class 96600.bd have rank \(0\).

Complex multiplication

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

Modular form 96600.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + 2 q^{13} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.