# Properties

 Label 72450.ei Number of curves $2$ Conductor $72450$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ei1")

sage: E.isogeny_class()

## Elliptic curves in class 72450.ei

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.ei1 72450dc2 $$[1, -1, 1, -13970, 632457]$$ $$89332607016927/1060723384$$ $$3579941421000$$ $$[2]$$ $$147456$$ $$1.2205$$
72450.ei2 72450dc1 $$[1, -1, 1, -170, 25257]$$ $$-160103007/81288256$$ $$-274347864000$$ $$[2]$$ $$73728$$ $$0.87390$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 72450.ei have rank $$1$$.

## Complex multiplication

The elliptic curves in class 72450.ei do not have complex multiplication.

## Modular form 72450.2.a.ei

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} - 2q^{11} + 2q^{13} + q^{14} + q^{16} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.