# Properties

 Label 270802.p Number of curves $2$ Conductor $270802$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 270802.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.p1 270802p2 $$[1, -1, 1, -195270, 2877179]$$ $$1384331873625/795308122$$ $$473067818346313162$$ $$$$ $$2795520$$ $$2.0811$$
270802.p2 270802p1 $$[1, -1, 1, 48620, 340723]$$ $$21369234375/12456892$$ $$-7409649868778332$$ $$$$ $$1397760$$ $$1.7346$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 270802.p have rank $$1$$.

## Complex multiplication

The elliptic curves in class 270802.p do not have complex multiplication.

## Modular form 270802.2.a.p

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} - 3q^{9} + 4q^{11} - 4q^{13} - q^{14} + q^{16} + 4q^{17} - 3q^{18} + 4q^{19} + O(q^{20})$$ ## 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. 