Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.bs1 31200bw2 \([0, 1, 0, -33008, 2296488]\) \(497169541448/190125\) \(1521000000000\) \([2]\) \(92160\) \(1.3034\)  
31200.bs2 31200bw1 \([0, 1, 0, -1758, 46488]\) \(-601211584/609375\) \(-609375000000\) \([2]\) \(46080\) \(0.95688\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 31200.2.a.bs

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