# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 379050.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.r1 379050r1 $$[1, 1, 0, -726700, -29006000]$$ $$461889917/263424$$ $$24205105774500000000$$ $$$$ $$12579840$$ $$2.4092$$ $$\Gamma_0(N)$$-optimal
379050.r2 379050r2 $$[1, 1, 0, 2883300, -227556000]$$ $$28849701763/16941456$$ $$-1556690865122531250000$$ $$$$ $$25159680$$ $$2.7558$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 379050.2.a.r

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 2q^{11} - q^{12} - 6q^{13} + q^{14} + q^{16} + 4q^{17} - q^{18} + O(q^{20})$$ ## 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 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. 