# Properties

 Label 235950.ip Number of curves $2$ Conductor $235950$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ip1")

sage: E.isogeny_class()

## Elliptic curves in class 235950.ip

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.ip1 235950ip2 $$[1, 0, 0, -139213, 17898167]$$ $$10779215329/1232010$$ $$34102826056406250$$ $$[2]$$ $$2949120$$ $$1.9046$$
235950.ip2 235950ip1 $$[1, 0, 0, 12037, 1411917]$$ $$6967871/35100$$ $$-971590485937500$$ $$[2]$$ $$1474560$$ $$1.5580$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 235950.ip have rank $$0$$.

## Complex multiplication

The elliptic curves in class 235950.ip do not have complex multiplication.

## Modular form 235950.2.a.ip

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} + q^{8} + q^{9} + q^{12} - q^{13} + 2q^{14} + q^{16} + 8q^{17} + q^{18} + 6q^{19} + O(q^{20})$$

## 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.