Properties

Label 172480.q
Number of curves $4$
Conductor $172480$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 172480.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
172480.q1 172480ep4 \([0, 1, 0, -81899841, 277169852959]\) \(1969902499564819009/63690429687500\) \(1964275233536000000000000\) \([2]\) \(31850496\) \(3.4353\)  
172480.q2 172480ep2 \([0, 1, 0, -11214401, -14330140385]\) \(5057359576472449/51765560000\) \(1596500572488335360000\) \([2]\) \(10616832\) \(2.8860\)  
172480.q3 172480ep1 \([0, 1, 0, -175681, -551610081]\) \(-19443408769/4249907200\) \(-131071300645106483200\) \([2]\) \(5308416\) \(2.5395\) \(\Gamma_0(N)\)-optimal
172480.q4 172480ep3 \([0, 1, 0, 1580479, 14857991455]\) \(14156681599871/3100231750000\) \(-95614183710588928000000\) \([2]\) \(15925248\) \(3.0888\)  

Rank

sage: E.rank()
 

The elliptic curves in class 172480.q have rank \(1\).

Complex multiplication

The elliptic curves in class 172480.q do not have complex multiplication.

Modular form 172480.2.a.q

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.