# Properties

 Label 5445.e Number of curves $2$ Conductor $5445$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5445.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5445.e1 5445j1 $$[1, -1, 1, -122, 344]$$ $$205379/75$$ $$72772425$$ $$$$ $$1536$$ $$0.20893$$ $$\Gamma_0(N)$$-optimal
5445.e2 5445j2 $$[1, -1, 1, 373, 2126]$$ $$5929741/5625$$ $$-5457931875$$ $$$$ $$3072$$ $$0.55551$$

## Rank

sage: E.rank()

The elliptic curves in class 5445.e have rank $$1$$.

## Complex multiplication

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

## Modular form5445.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + q^{5} + 2q^{7} + 3q^{8} - q^{10} - 4q^{13} - 2q^{14} - q^{16} - 6q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 