# Properties

 Label 87120.fd Number of curves $2$ Conductor $87120$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("fd1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.fd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.fd1 87120fp2 $$[0, 0, 0, -104392992, -410540433424]$$ $$-196566176333824/421875$$ $$-270030454702272000000$$ $$[]$$ $$8211456$$ $$3.1679$$
87120.fd2 87120fp1 $$[0, 0, 0, -894432, -913832656]$$ $$-123633664/492075$$ $$-314963522364730060800$$ $$[]$$ $$2737152$$ $$2.6186$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 87120.fd have rank $$1$$.

## Complex multiplication

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

## Modular form 87120.2.a.fd

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 