Properties

Label 6720.bh
Number of curves $4$
Conductor $6720$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6720.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6720.bh1 6720r3 \([0, 1, 0, -336001, -75077185]\) \(128025588102048008/7875\) \(258048000\) \([2]\) \(24576\) \(1.5225\)  
6720.bh2 6720r4 \([0, 1, 0, -23521, -880321]\) \(43919722445768/15380859375\) \(504000000000000\) \([2]\) \(24576\) \(1.5225\)  
6720.bh3 6720r2 \([0, 1, 0, -21001, -1178185]\) \(250094631024064/62015625\) \(254016000000\) \([2, 2]\) \(12288\) \(1.1760\)  
6720.bh4 6720r1 \([0, 1, 0, -1156, -23206]\) \(-2671731885376/1969120125\) \(-126023688000\) \([2]\) \(6144\) \(0.82939\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6720.bh have rank \(0\).

Complex multiplication

The elliptic curves in class 6720.bh do not have complex multiplication.

Modular form 6720.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 2q^{17} - 8q^{19} + O(q^{20})\)  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.