# Properties

 Label 348075n Number of curves $2$ Conductor $348075$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 348075n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348075.n1 348075n1 $$[1, -1, 1, -102380, -12576378]$$ $$10418796526321/6390657$$ $$72793577390625$$ $$$$ $$1433600$$ $$1.6027$$ $$\Gamma_0(N)$$-optimal
348075.n2 348075n2 $$[1, -1, 1, -83255, -17434128]$$ $$-5602762882081/8312741073$$ $$-94687316284640625$$ $$$$ $$2867200$$ $$1.9492$$

## Rank

sage: E.rank()

The elliptic curves in class 348075n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 348075n do not have complex multiplication.

## Modular form 348075.2.a.n

sage: E.q_eigenform(10)

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