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Properties

Label 31200.bt
Number of curves $2$
Conductor $31200$
CM no
Rank $1$
Graph

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

Elliptic curves in class 31200.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.bt1 31200bx2 \([0, 1, 0, -32833, -2299537]\) \(61162984000/41067\) \(2628288000000\) \([2]\) \(92160\) \(1.3215\)  
31200.bt2 31200bx1 \([0, 1, 0, -2458, -21412]\) \(1643032000/767637\) \(767637000000\) \([2]\) \(46080\) \(0.97496\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 31200.bt have rank \(1\).

Complex multiplication

The elliptic curves in class 31200.bt do not have complex multiplication.

Modular form 31200.2.a.bt

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{7} + q^{9} + 4 q^{11} - q^{13} + 6 q^{17} + 6 q^{19} + O(q^{20})\) 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.