# Properties

 Label 101430.dz Number of curves $2$ Conductor $101430$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dz1")

sage: E.isogeny_class()

## Elliptic curves in class 101430.dz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.dz1 101430cz1 $$[1, -1, 1, -241403483, 603658895627]$$ $$489781415227546051766883/233890092903563264000$$ $$742957259580305490051072000$$ $$[2]$$ $$49545216$$ $$3.8499$$ $$\Gamma_0(N)$$-optimal
101430.dz2 101430cz2 $$[1, -1, 1, 866482597, 4590719320331]$$ $$22649115256119592694355357/15973509811739648000000$$ $$-50740221307716661883904000000$$ $$[2]$$ $$99090432$$ $$4.1965$$

## Rank

sage: E.rank()

The elliptic curves in class 101430.dz have rank $$0$$.

## Complex multiplication

The elliptic curves in class 101430.dz do not have complex multiplication.

## Modular form 101430.2.a.dz

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 2q^{11} + 6q^{13} + q^{16} + 6q^{17} + O(q^{20})$$

## 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.