Properties

Label 8400bt
Number of curves $2$
Conductor $8400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.bd1 8400bt1 \([0, -1, 0, -2728, -53648]\) \(4386781853/27216\) \(13934592000\) \([2]\) \(7680\) \(0.78449\) \(\Gamma_0(N)\)-optimal
8400.bd2 8400bt2 \([0, -1, 0, -1128, -117648]\) \(-310288733/11573604\) \(-5925685248000\) \([2]\) \(15360\) \(1.1311\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8400bt have rank \(0\).

Complex multiplication

The elliptic curves in class 8400bt do not have complex multiplication.

Modular form 8400.2.a.bt

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + 2 q^{11} - 2 q^{13} - 8 q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.