# Properties

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

# Learn more

Show commands for: SageMath
sage: E = EllipticCurve("cf1")

sage: E.isogeny_class()

## Elliptic curves in class 101430.cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.cf1 101430l1 $$[1, -1, 0, -62484, 5913088]$$ $$8493409990827/185150000$$ $$588133233450000$$ $$[2]$$ $$491520$$ $$1.6223$$ $$\Gamma_0(N)$$-optimal
101430.cf2 101430l2 $$[1, -1, 0, 5136, 17990020]$$ $$4716275733/44023437500$$ $$-139841461757812500$$ $$[2]$$ $$983040$$ $$1.9689$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 101430.2.a.cf

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.