Properties

Label 69360.dh
Number of curves $2$
Conductor $69360$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dh1")
 
E.isogeny_class()
 

Elliptic curves in class 69360.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69360.dh1 69360dq1 \([0, 1, 0, -1745, -28650]\) \(-127157223424/16875\) \(-78030000\) \([]\) \(31104\) \(0.53393\) \(\Gamma_0(N)\)-optimal
69360.dh2 69360dq2 \([0, 1, 0, 295, -88422]\) \(611926016/732421875\) \(-3386718750000\) \([]\) \(93312\) \(1.0832\)  

Rank

sage: E.rank()
 

The elliptic curves in class 69360.dh have rank \(0\).

Complex multiplication

The elliptic curves in class 69360.dh do not have complex multiplication.

Modular form 69360.2.a.dh

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.