# Properties

 Label 101430.db Number of curves $2$ Conductor $101430$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("db1")

sage: E.isogeny_class()

## Elliptic curves in class 101430.db

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.db1 101430da1 $$[1, -1, 1, -562358, -159091019]$$ $$8493409990827/185150000$$ $$428749127185050000$$ $$$$ $$1474560$$ $$2.1716$$ $$\Gamma_0(N)$$-optimal
101430.db2 101430da2 $$[1, -1, 1, 46222, -485776763]$$ $$4716275733/44023437500$$ $$-101944425621445312500$$ $$$$ $$2949120$$ $$2.5182$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 101430.2.a.db

sage: E.q_eigenform(10)

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