# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 72450.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.h1 72450d1 $$[1, -1, 0, -3792, 77616]$$ $$14295828483/2254000$$ $$950906250000$$ $$$$ $$110592$$ $$1.0212$$ $$\Gamma_0(N)$$-optimal
72450.h2 72450d2 $$[1, -1, 0, 6708, 424116]$$ $$79119341757/231437500$$ $$-97637695312500$$ $$$$ $$221184$$ $$1.3678$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 72450.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} - 4q^{11} + q^{14} + q^{16} + 6q^{17} + O(q^{20})$$ ## 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. 