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Properties

Label 55545.v
Number of curves $4$
Conductor $55545$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 55545.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55545.v1 55545t4 \([1, 0, 1, -2271273, -1317693389]\) \(8753151307882969/65205\) \(9652680142245\) \([2]\) \(743424\) \(2.0861\)  
55545.v2 55545t2 \([1, 0, 1, -142048, -20569519]\) \(2141202151369/5832225\) \(863378612723025\) \([2, 2]\) \(371712\) \(1.7395\)  
55545.v3 55545t3 \([1, 0, 1, -86503, -36810877]\) \(-483551781049/3672913125\) \(-543722959679143125\) \([2]\) \(743424\) \(2.0861\)  
55545.v4 55545t1 \([1, 0, 1, -12443, -40087]\) \(1439069689/828345\) \(122624788473705\) \([2]\) \(185856\) \(1.3929\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 55545.v have rank \(0\).

Complex multiplication

The elliptic curves in class 55545.v do not have complex multiplication.

Modular form 55545.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{7} - 3 q^{8} + q^{9} + q^{10} + 4 q^{11} - q^{12} + 2 q^{13} - q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.