# Properties

 Label 5445.i Number of curves $4$ Conductor $5445$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("i1")

E.isogeny_class()

## Elliptic curves in class 5445.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5445.i1 5445e4 $$[1, -1, 0, -64455, 6312950]$$ $$22930509321/6875$$ $$8878842286875$$ $$[2]$$ $$15360$$ $$1.4626$$
5445.i2 5445e3 $$[1, -1, 0, -31785, -2122444]$$ $$2749884201/73205$$ $$94541912670645$$ $$[2]$$ $$15360$$ $$1.4626$$
5445.i3 5445e2 $$[1, -1, 0, -4560, 71891]$$ $$8120601/3025$$ $$3906690606225$$ $$[2, 2]$$ $$7680$$ $$1.1160$$
5445.i4 5445e1 $$[1, -1, 0, 885, 7640]$$ $$59319/55$$ $$-71030738295$$ $$[2]$$ $$3840$$ $$0.76944$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5445.2.a.i

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.