Properties

Label 154560.ge
Number of curves $2$
Conductor $154560$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ge1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 154560.ge

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.ge1 154560fj1 \([0, 1, 0, -15681, 716319]\) \(1626794704081/83462400\) \(21879167385600\) \([2]\) \(589824\) \(1.3176\) \(\Gamma_0(N)\)-optimal
154560.ge2 154560fj2 \([0, 1, 0, 9919, 2851359]\) \(411664745519/13605414480\) \(-3566577773445120\) \([2]\) \(1179648\) \(1.6642\)  

Rank

sage: E.rank()
 

The elliptic curves in class 154560.ge have rank \(0\).

Complex multiplication

The elliptic curves in class 154560.ge do not have complex multiplication.

Modular form 154560.2.a.ge

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{7} + q^{9} + 6q^{11} - q^{15} + 6q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.