# Properties

 Label 1800.d Number of curves $2$ Conductor $1800$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 1800.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1800.d1 1800q2 $$[0, 0, 0, -315, 2150]$$ $$1000188$$ $$3456000$$ $$[2]$$ $$512$$ $$0.17407$$
1800.d2 1800q1 $$[0, 0, 0, -15, 50]$$ $$-432$$ $$-864000$$ $$[2]$$ $$256$$ $$-0.17250$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1800.d have rank $$1$$.

## Complex multiplication

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

## Modular form1800.2.a.d

sage: E.q_eigenform(10)

$$q - 4q^{7} + 4q^{11} + 4q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.