# Properties

 Label 333270.ev Number of curves $2$ Conductor $333270$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ev1")

sage: E.isogeny_class()

## Elliptic curves in class 333270.ev

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333270.ev1 333270ev2 $$[1, -1, 1, -178292, 25468759]$$ $$70665260180607/9411920000$$ $$83481311536560000$$ $$$$ $$4128768$$ $$1.9747$$
333270.ev2 333270ev1 $$[1, -1, 1, -45812, -3358889]$$ $$1198785674367/140492800$$ $$1246135029350400$$ $$$$ $$2064384$$ $$1.6281$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 333270.ev have rank $$2$$.

## Complex multiplication

The elliptic curves in class 333270.ev do not have complex multiplication.

## Modular form 333270.2.a.ev

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} - 2q^{11} - 4q^{13} + q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 