Properties

Label 55545.t
Number of curves $4$
Conductor $55545$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 55545.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55545.t1 55545g4 \([1, 0, 1, -59524, 5584241]\) \(157551496201/13125\) \(1942971043125\) \([2]\) \(180224\) \(1.4018\)  
55545.t2 55545g2 \([1, 0, 1, -3979, 74177]\) \(47045881/11025\) \(1632095676225\) \([2, 2]\) \(90112\) \(1.0552\)  
55545.t3 55545g1 \([1, 0, 1, -1334, -17869]\) \(1771561/105\) \(15543768345\) \([2]\) \(45056\) \(0.70864\) \(\Gamma_0(N)\)-optimal
55545.t4 55545g3 \([1, 0, 1, 9246, 465637]\) \(590589719/972405\) \(-143950838643045\) \([2]\) \(180224\) \(1.4018\)  

Rank

sage: E.rank()
 

The elliptic curves in class 55545.t have rank \(1\).

Complex multiplication

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

Modular form 55545.2.a.t

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