# Properties

 Label 9075.j Number of curves $2$ Conductor $9075$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 9075.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9075.j1 9075g2 $$[0, -1, 1, -149783, 22362218]$$ $$-196566176333824/421875$$ $$-797607421875$$ $$[]$$ $$31104$$ $$1.5312$$
9075.j2 9075g1 $$[0, -1, 1, -1283, 50093]$$ $$-123633664/492075$$ $$-930329296875$$ $$[]$$ $$10368$$ $$0.98194$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9075.j have rank $$0$$.

## Complex multiplication

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

## Modular form9075.2.a.j

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 