# Properties

 Label 14994bg Number of curves $4$ Conductor $14994$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 14994bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14994.h4 14994bg1 $$[1, -1, 0, 432, 933120]$$ $$103823/4386816$$ $$-376240191860736$$ $$$$ $$73728$$ $$1.4757$$ $$\Gamma_0(N)$$-optimal
14994.h3 14994bg2 $$[1, -1, 0, -140688, 19984320]$$ $$3590714269297/73410624$$ $$6296144460669504$$ $$[2, 2]$$ $$147456$$ $$1.8222$$
14994.h2 14994bg3 $$[1, -1, 0, -299448, -33263784]$$ $$34623662831857/14438442312$$ $$1238329190382511752$$ $$$$ $$294912$$ $$2.1688$$
14994.h1 14994bg4 $$[1, -1, 0, -2239848, 1290815784]$$ $$14489843500598257/6246072$$ $$535701366926712$$ $$$$ $$294912$$ $$2.1688$$

## Rank

sage: E.rank()

The elliptic curves in class 14994bg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 14994bg do not have complex multiplication.

## Modular form 14994.2.a.bg

sage: E.q_eigenform(10)

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