# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 72450.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.u1 72450w1 $$[1, -1, 0, -5292, -80384]$$ $$1439069689/579600$$ $$6602006250000$$ $$[2]$$ $$147456$$ $$1.1578$$ $$\Gamma_0(N)$$-optimal
72450.u2 72450w2 $$[1, -1, 0, 17208, -597884]$$ $$49471280711/41992020$$ $$-478315352812500$$ $$[2]$$ $$294912$$ $$1.5044$$

## Rank

sage: E.rank()

The elliptic curves in class 72450.u have rank $$2$$.

## Complex multiplication

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

## Modular form 72450.2.a.u

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} + 2q^{11} - 4q^{13} + q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.