Properties

Label 87120.e
Number of curves $4$
Conductor $87120$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.e1 87120bk4 \([0, 0, 0, -116523, 15309162]\) \(132304644/5\) \(6612316001280\) \([2]\) \(327680\) \(1.5460\)  
87120.e2 87120bk2 \([0, 0, 0, -7623, 215622]\) \(148176/25\) \(8265395001600\) \([2, 2]\) \(163840\) \(1.1995\)  
87120.e3 87120bk1 \([0, 0, 0, -2178, -35937]\) \(55296/5\) \(103317437520\) \([2]\) \(81920\) \(0.85289\) \(\Gamma_0(N)\)-optimal
87120.e4 87120bk3 \([0, 0, 0, 14157, 1221858]\) \(237276/625\) \(-826539500160000\) \([2]\) \(327680\) \(1.5460\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 87120.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.