# Properties

 Label 5445.f Number of curves $2$ Conductor $5445$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 5445.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5445.f1 5445l2 $$[0, 0, 1, -6524562, 6414694272]$$ $$-196566176333824/421875$$ $$-65925403980046875$$ $$$$ $$114048$$ $$2.4748$$
5445.f2 5445l1 $$[0, 0, 1, -55902, 14278635]$$ $$-123633664/492075$$ $$-76895391202326675$$ $$[]$$ $$38016$$ $$1.9255$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5445.f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5445.f do not have complex multiplication.

## Modular form5445.2.a.f

sage: E.q_eigenform(10)

$$q - 2q^{4} + q^{5} - q^{7} + 2q^{13} + 4q^{16} - 6q^{17} - 7q^{19} + O(q^{20})$$ ## 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. 