# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 72450.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.m1 72450bf2 $$[1, -1, 0, -95067, -6265409]$$ $$8341959848041/3327411150$$ $$37901292630468750$$ $$$$ $$737280$$ $$1.8793$$
72450.m2 72450bf1 $$[1, -1, 0, -43317, 3411841]$$ $$789145184521/17996580$$ $$204992294062500$$ $$$$ $$368640$$ $$1.5328$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 72450.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} - 2q^{11} + 2q^{13} + q^{14} + q^{16} - 6q^{19} + O(q^{20})$$ ## 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. 