Properties

Label 32340.w
Number of curves $2$
Conductor $32340$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32340.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.w1 32340bc2 \([0, 1, 0, -89196, -9905820]\) \(2605772594896/108945375\) \(3281232492384000\) \([2]\) \(165888\) \(1.7421\)  
32340.w2 32340bc1 \([0, 1, 0, 2679, -571320]\) \(1129201664/75796875\) \(-142678824750000\) \([2]\) \(82944\) \(1.3956\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32340.w have rank \(0\).

Complex multiplication

The elliptic curves in class 32340.w do not have complex multiplication.

Modular form 32340.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} - q^{11} - 4q^{13} - q^{15} - 2q^{17} + 6q^{19} + O(q^{20})\)  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.