# Properties

 Label 72450.g Number of curves $2$ Conductor $72450$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 72450.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.g1 72450ba2 $$[1, -1, 0, -136242, -18087084]$$ $$24553362849625/1755162752$$ $$19992400722000000$$ $$$$ $$774144$$ $$1.8748$$
72450.g2 72450ba1 $$[1, -1, 0, 7758, -1239084]$$ $$4533086375/60669952$$ $$-691068672000000$$ $$$$ $$387072$$ $$1.5282$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 72450.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} - 4q^{11} + q^{14} + q^{16} + 6q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 