Properties

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

Related objects

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)

$$q + q^{5} + 2q^{7} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

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.