# Properties

 Label 72450.dh Number of curves $2$ Conductor $72450$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dh1")

sage: E.isogeny_class()

## Elliptic curves in class 72450.dh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.dh1 72450cl1 $$[1, -1, 1, -31880, -2141253]$$ $$8493409990827/185150000$$ $$78110156250000$$ $$$$ $$245760$$ $$1.4540$$ $$\Gamma_0(N)$$-optimal
72450.dh2 72450cl2 $$[1, -1, 1, 2620, -6557253]$$ $$4716275733/44023437500$$ $$-18572387695312500$$ $$$$ $$491520$$ $$1.8006$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 72450.2.a.dh

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. 