# Properties

 Label 1800g Number of curves 4 Conductor 1800 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1800.v1")

sage: E.isogeny_class()

## Elliptic curves in class 1800g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1800.v3 1800g1 [0, 0, 0, -450, -3375]  768 $$\Gamma_0(N)$$-optimal
1800.v2 1800g2 [0, 0, 0, -1575, 20250] [2, 2] 1536
1800.v1 1800g3 [0, 0, 0, -24075, 1437750]  3072
1800.v4 1800g4 [0, 0, 0, 2925, 114750]  3072

## Rank

sage: E.rank()

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

## 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 Cremona 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 Cremona labels. 