Properties

Label 333270.bq
Number of curves $4$
Conductor $333270$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 333270.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.bq1 333270bq3 \([1, -1, 0, -175776596199, 28364484932214493]\) \(5565604209893236690185614401/229307220930246900000\) \(24746414064001281479794698900000\) \([2]\) \(2595225600\) \(5.1052\)  
333270.bq2 333270bq4 \([1, -1, 0, -53588768679, -4403281083996515]\) \(157706830105239346386477121/13650704956054687500000\) \(1473159003618124703979492187500000\) \([2]\) \(2595225600\) \(5.1052\)  
333270.bq3 333270bq2 \([1, -1, 0, -11522096199, 397561086114493]\) \(1567558142704512417614401/274462175610000000000\) \(29619453827046040654410000000000\) \([2, 2]\) \(1297612800\) \(4.7587\)  
333270.bq4 333270bq1 \([1, -1, 0, 1372977081, 35588642100925]\) \(2652277923951208297919/6605028468326400000\) \(-712802539399496078337638400000\) \([2]\) \(648806400\) \(4.4121\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 333270.bq have rank \(0\).

Complex multiplication

The elliptic curves in class 333270.bq do not have complex multiplication.

Modular form 333270.2.a.bq

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - 6q^{13} + q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.