# Properties

 Label 1800.v Number of curves $4$ Conductor $1800$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 1800.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1800.v1 1800g3 $$[0, 0, 0, -24075, 1437750]$$ $$132304644/5$$ $$58320000000$$ $$$$ $$3072$$ $$1.1518$$
1800.v2 1800g2 $$[0, 0, 0, -1575, 20250]$$ $$148176/25$$ $$72900000000$$ $$[2, 2]$$ $$1536$$ $$0.80524$$
1800.v3 1800g1 $$[0, 0, 0, -450, -3375]$$ $$55296/5$$ $$911250000$$ $$$$ $$768$$ $$0.45866$$ $$\Gamma_0(N)$$-optimal
1800.v4 1800g4 $$[0, 0, 0, 2925, 114750]$$ $$237276/625$$ $$-7290000000000$$ $$$$ $$3072$$ $$1.1518$$

## Rank

sage: E.rank()

The elliptic curves in class 1800.v have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1800.v do not have complex multiplication.

## Modular form1800.2.a.v

sage: E.q_eigenform(10)

$$q + 4q^{7} - 4q^{11} + 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 