# Properties

 Label 300.a Number of curves $2$ Conductor $300$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 300.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
300.a1 300d1 $$[0, -1, 0, -13, 22]$$ $$131072/9$$ $$18000$$ $$$$ $$24$$ $$-0.43525$$ $$\Gamma_0(N)$$-optimal
300.a2 300d2 $$[0, -1, 0, 12, 72]$$ $$5488/81$$ $$-2592000$$ $$$$ $$48$$ $$-0.088679$$

## Rank

sage: E.rank()

The elliptic curves in class 300.a have rank $$1$$.

## Complex multiplication

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

## Modular form300.2.a.a

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. 