# Properties

 Label 379050y Number of curves $2$ Conductor $379050$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 379050y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.y1 379050y1 $$[1, 1, 0, -164775, -25797375]$$ $$4616586342451/3307500$$ $$354470976562500$$ $$$$ $$3317760$$ $$1.7271$$ $$\Gamma_0(N)$$-optimal
379050.y2 379050y2 $$[1, 1, 0, -131525, -36470625]$$ $$-2347864201171/3986718750$$ $$-427264123535156250$$ $$$$ $$6635520$$ $$2.0737$$

## Rank

sage: E.rank()

The elliptic curves in class 379050y have rank $$1$$.

## Complex multiplication

The elliptic curves in class 379050y do not have complex multiplication.

## Modular form 379050.2.a.y

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 4q^{11} - q^{12} + q^{14} + q^{16} + 4q^{17} - q^{18} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 