# Properties

 Label 468.d Number of curves $2$ Conductor $468$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 468.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
468.d1 468e2 $$[0, 0, 0, -183, 830]$$ $$3631696/507$$ $$94618368$$ $$$$ $$192$$ $$0.25678$$
468.d2 468e1 $$[0, 0, 0, -48, -115]$$ $$1048576/117$$ $$1364688$$ $$$$ $$96$$ $$-0.089794$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 468.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 468.d do not have complex multiplication.

## Modular form468.2.a.d

sage: E.q_eigenform(10)

$$q + 4q^{5} - 2q^{7} + 4q^{11} + q^{13} - 2q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 