# Properties

 Label 72450.dg Number of curves $2$ Conductor $72450$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dg1")

sage: E.isogeny_class()

## Elliptic curves in class 72450.dg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.dg1 72450cy2 $$[1, -1, 1, -3143180, -2121970553]$$ $$89332607016927/1060723384$$ $$40777770248578125000$$ $$[2]$$ $$2211840$$ $$2.5745$$
72450.dg2 72450cy1 $$[1, -1, 1, -38180, -85090553]$$ $$-160103007/81288256$$ $$-3124993638375000000$$ $$[2]$$ $$1105920$$ $$2.2279$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 72450.dg have rank $$0$$.

## Complex multiplication

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

## Modular form 72450.2.a.dg

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.