# Properties

 Label 114444.p Number of curves 2 Conductor 114444 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("114444.p1")

sage: E.isogeny_class()

## Elliptic curves in class 114444.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
114444.p1 114444p2 [0, 0, 0, -32079, 1051382]  473088
114444.p2 114444p1 [0, 0, 0, 6936, 122825]  236544 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 114444.p have rank $$0$$.

## Modular form 114444.2.a.p

sage: E.q_eigenform(10)

$$q + 2q^{5} + 2q^{7} + q^{11} - 2q^{13} - 6q^{19} + O(q^{20})$$

## 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. 