# Properties

 Label 270802v Number of curves $2$ Conductor $270802$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 270802v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.v2 270802v1 $$[1, 1, 1, 32361, -7960675]$$ $$6300872423/49827568$$ $$-29638599475113328$$ $$[2]$$ $$2150400$$ $$1.8421$$ $$\Gamma_0(N)$$-optimal
270802.v1 270802v2 $$[1, 1, 1, -455419, -108833579]$$ $$17561807821657/1590616244$$ $$946135636692626324$$ $$[2]$$ $$4300800$$ $$2.1887$$

## Rank

sage: E.rank()

The elliptic curves in class 270802v have rank $$0$$.

## Complex multiplication

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

## Modular form 270802.2.a.v

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} - 2q^{5} + 2q^{6} + q^{7} + q^{8} + q^{9} - 2q^{10} + 2q^{12} + 2q^{13} + q^{14} - 4q^{15} + q^{16} + q^{18} + 6q^{19} + O(q^{20})$$

## 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 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.