# Properties

 Label 348726.x Number of curves $2$ Conductor $348726$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 348726.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348726.x1 348726x1 $$[1, 0, 1, -548006, -145152520]$$ $$56402207875/4451328$$ $$1436388784379200512$$ $$$$ $$5836800$$ $$2.2278$$ $$\Gamma_0(N)$$-optimal
348726.x2 348726x2 $$[1, 0, 1, 549434, -653486728]$$ $$56844576125/604685088$$ $$-195124438928012019552$$ $$$$ $$11673600$$ $$2.5744$$

## Rank

sage: E.rank()

The elliptic curves in class 348726.x have rank $$1$$.

## Complex multiplication

The elliptic curves in class 348726.x do not have complex multiplication.

## Modular form 348726.2.a.x

sage: E.q_eigenform(10)

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