# Properties

 Label 348726.n Number of curves $2$ Conductor $348726$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 348726.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
348726.n1 348726n1 [1, 0, 1, -366139565, 2696585928680] [3] 106375680 $$\Gamma_0(N)$$-optimal
348726.n2 348726n2 [1, 0, 1, -242986220, 4536447641642] [] 319127040

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 348726.2.a.n

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - 3q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + 3q^{10} + 3q^{11} + q^{12} - 4q^{13} - q^{14} - 3q^{15} + q^{16} + 3q^{17} - q^{18} + O(q^{20})$$

## 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.