Properties

Label 87120.ed
Number of curves $2$
Conductor $87120$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ed1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.ed1 87120bt2 \([0, 0, 0, -388115607, -2942996692394]\) \(14692827276345584/6075\) \(2673301501552492800\) \([2]\) \(8110080\) \(3.3179\)  
87120.ed2 87120bt1 \([0, 0, 0, -24253482, -45999225569]\) \(-57367289145344/36905625\) \(-1015019163870712110000\) \([2]\) \(4055040\) \(2.9713\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87120.ed have rank \(1\).

Complex multiplication

The elliptic curves in class 87120.ed do not have complex multiplication.

Modular form 87120.2.a.ed

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2q^{7} + 4q^{13} - 2q^{17} + 2q^{19} + O(q^{20})\)  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.