# Properties

 Label 300.d Number of curves $2$ Conductor $300$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 300.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
300.d1 300c1 $$[0, 1, 0, -333, 2088]$$ $$131072/9$$ $$281250000$$ $$$$ $$120$$ $$0.36947$$ $$\Gamma_0(N)$$-optimal
300.d2 300c2 $$[0, 1, 0, 292, 9588]$$ $$5488/81$$ $$-40500000000$$ $$$$ $$240$$ $$0.71604$$

## Rank

sage: E.rank()

The elliptic curves in class 300.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 300.d do not have complex multiplication.

## Modular form300.2.a.d

sage: E.q_eigenform(10)

$$q + q^{3} + 4q^{7} + q^{9} - 4q^{11} + 4q^{17} + O(q^{20})$$ ## 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. 