# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("ds1")

sage: E.isogeny_class()

## Elliptic curves in class 379050.ds

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.ds1 379050ds2 $$[1, 0, 1, -3163451, 2291105798]$$ $$-7620530425/526848$$ $$-242051057745000000000$$ $$[]$$ $$22394880$$ $$2.6623$$
379050.ds2 379050ds1 $$[1, 0, 1, 220924, 3268298]$$ $$2595575/1512$$ $$-694661836640625000$$ $$[]$$ $$7464960$$ $$2.1129$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 379050.2.a.ds

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 