# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 127050v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.bm2 127050v1 $$[1, 1, 0, 74050, 661500]$$ $$2595575/1512$$ $$-26158205390625000$$ $$[]$$ $$1166400$$ $$1.8397$$ $$\Gamma_0(N)$$-optimal
127050.bm1 127050v2 $$[1, 1, 0, -1060325, 444202125]$$ $$-7620530425/526848$$ $$-9114681345000000000$$ $$[]$$ $$3499200$$ $$2.3890$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 127050.2.a.v

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 Cremona 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 Cremona labels. 