Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("fn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.fn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.fn1 87120fz3 \([0, 0, 0, -45012, 3674891]\) \(488095744/125\) \(2582935938000\) \([2]\) \(207360\) \(1.3676\)  
87120.fn2 87120fz4 \([0, 0, 0, -39567, 4597274]\) \(-20720464/15625\) \(-5165871876000000\) \([2]\) \(414720\) \(1.7142\)  
87120.fn3 87120fz1 \([0, 0, 0, -1452, -14641]\) \(16384/5\) \(103317437520\) \([2]\) \(69120\) \(0.81830\) \(\Gamma_0(N)\)-optimal
87120.fn4 87120fz2 \([0, 0, 0, 3993, -98494]\) \(21296/25\) \(-8265395001600\) \([2]\) \(138240\) \(1.1649\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 87120.2.a.fn

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2q^{7} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.