# Properties

 Label 270802h Number of curves $2$ Conductor $270802$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 270802h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.h2 270802h1 $$[1, 1, 0, -11791, 121125]$$ $$304821217/164864$$ $$98064951993344$$ $$$$ $$1003520$$ $$1.3757$$ $$\Gamma_0(N)$$-optimal
270802.h1 270802h2 $$[1, 1, 0, -146351, 21462341]$$ $$582810602977/829472$$ $$493389289716512$$ $$$$ $$2007040$$ $$1.7223$$

## Rank

sage: E.rank()

The elliptic curves in class 270802h have rank $$2$$.

## Complex multiplication

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

## Modular form 270802.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - 2q^{5} - 2q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} + 2q^{11} + 2q^{12} - 4q^{13} + q^{14} - 4q^{15} + q^{16} + 6q^{17} - q^{18} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 