# Properties

 Label 127050.hu Number of curves $2$ Conductor $127050$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hu1")

sage: E.isogeny_class()

## Elliptic curves in class 127050.hu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.hu1 127050io2 $$[1, 0, 0, -42413, 3553617]$$ $$-7620530425/526848$$ $$-583339606080000$$ $$[]$$ $$699840$$ $$1.5843$$
127050.hu2 127050io1 $$[1, 0, 0, 2962, 5292]$$ $$2595575/1512$$ $$-1674125145000$$ $$[]$$ $$233280$$ $$1.0350$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 127050.hu have rank $$1$$.

## Complex multiplication

The elliptic curves in class 127050.hu do not have complex multiplication.

## Modular form 127050.2.a.hu

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} + q^{12} + q^{13} - q^{14} + q^{16} - 3q^{17} + q^{18} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 