# Properties

 Label 2254a Number of curves $2$ Conductor $2254$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 2254a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2254.a2 2254a1 $$[1, 0, 1, 1689, -125590]$$ $$4533086375/60669952$$ $$-7137759182848$$ $$$$ $$5376$$ $$1.1471$$ $$\Gamma_0(N)$$-optimal
2254.a1 2254a2 $$[1, 0, 1, -29671, -1844118]$$ $$24553362849625/1755162752$$ $$206493142610048$$ $$$$ $$10752$$ $$1.4937$$

## Rank

sage: E.rank()

The elliptic curves in class 2254a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2254a do not have complex multiplication.

## Modular form2254.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} + q^{4} + 2q^{6} - q^{8} + q^{9} + 4q^{11} - 2q^{12} + q^{16} - 6q^{17} - q^{18} + 6q^{19} + O(q^{20})$$ ## 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. 