# Properties

 Label 9075.n Number of curves $2$ Conductor $9075$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 9075.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9075.n1 9075b1 $$[1, 1, 0, -40900, 1916875]$$ $$205379/75$$ $$2763219950390625$$ $$$$ $$50688$$ $$1.6633$$ $$\Gamma_0(N)$$-optimal
9075.n2 9075b2 $$[1, 1, 0, 125475, 13729500]$$ $$5929741/5625$$ $$-207241496279296875$$ $$$$ $$101376$$ $$2.0099$$

## Rank

sage: E.rank()

The elliptic curves in class 9075.n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9075.n do not have complex multiplication.

## Modular form9075.2.a.n

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} - q^{6} + 2 q^{7} - 3 q^{8} + q^{9} + q^{12} - 4 q^{13} + 2 q^{14} - q^{16} + 6 q^{17} + q^{18} - 6 q^{19} + O(q^{20})$$

## 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. 