# Properties

 Label 54418f Number of curves $2$ Conductor $54418$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 54418f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54418.g2 54418f1 $$[1, 1, 1, 5827, 807763]$$ $$4533086375/60669952$$ $$-292842270343168$$ $$$$ $$263424$$ $$1.4567$$ $$\Gamma_0(N)$$-optimal
54418.g1 54418f2 $$[1, 1, 1, -102333, 11753555]$$ $$24553362849625/1755162752$$ $$8471835367818368$$ $$$$ $$526848$$ $$1.8032$$

## Rank

sage: E.rank()

The elliptic curves in class 54418f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 54418f do not have complex multiplication.

## Modular form 54418.2.a.f

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} - q^{7} + q^{8} + q^{9} - 4q^{11} + 2q^{12} - q^{14} + q^{16} + 6q^{17} + q^{18} + 6q^{19} + O(q^{20})$$ ## 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. 