# Properties

 Label 101430.dt Number of curves $2$ Conductor $101430$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dt1")

sage: E.isogeny_class()

## Elliptic curves in class 101430.dt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.dt1 101430eh1 $$[1, -1, 1, -10373, 226797]$$ $$1439069689/579600$$ $$49710043731600$$ $$[2]$$ $$294912$$ $$1.3261$$ $$\Gamma_0(N)$$-optimal
101430.dt2 101430eh2 $$[1, -1, 1, 33727, 1620357]$$ $$49471280711/41992020$$ $$-3601492668354420$$ $$[2]$$ $$589824$$ $$1.6726$$

## Rank

sage: E.rank()

The elliptic curves in class 101430.dt have rank $$1$$.

## Complex multiplication

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

## Modular form 101430.2.a.dt

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 2q^{11} - 4q^{13} + q^{16} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.