# Properties

 Label 324.d Number of curves $2$ Conductor $324$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 324.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
324.d1 324b2 $$[0, 0, 0, -351, -2538]$$ $$-316368$$ $$-15116544$$ $$[]$$ $$108$$ $$0.24475$$
324.d2 324b1 $$[0, 0, 0, 9, -18]$$ $$432$$ $$-186624$$ $$$$ $$36$$ $$-0.30456$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 324.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 324.d do not have complex multiplication.

## Modular form324.2.a.d

sage: E.q_eigenform(10)

$$q + 3 q^{5} + 2 q^{7} - 6 q^{11} + 5 q^{13} - 3 q^{17} + 2 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 