# Properties

 Label 142800ev Number of curves $4$ Conductor $142800$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 142800ev

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142800.bm4 142800ev1 $$[0, -1, 0, 392, -806288]$$ $$103823/4386816$$ $$-280756224000000$$ $$[2]$$ $$589824$$ $$1.4513$$ $$\Gamma_0(N)$$-optimal
142800.bm3 142800ev2 $$[0, -1, 0, -127608, -17190288]$$ $$3590714269297/73410624$$ $$4698279936000000$$ $$[2, 2]$$ $$1179648$$ $$1.7978$$
142800.bm2 142800ev3 $$[0, -1, 0, -271608, 28889712]$$ $$34623662831857/14438442312$$ $$924060307968000000$$ $$[2]$$ $$2359296$$ $$2.1444$$
142800.bm1 142800ev4 $$[0, -1, 0, -2031608, -1113894288]$$ $$14489843500598257/6246072$$ $$399748608000000$$ $$[2]$$ $$2359296$$ $$2.1444$$

## Rank

sage: E.rank()

The elliptic curves in class 142800ev have rank $$0$$.

## Complex multiplication

The elliptic curves in class 142800ev do not have complex multiplication.

## Modular form 142800.2.a.ev

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} + 6q^{13} - q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.