# Properties

 Label 55440.en Number of curves $2$ Conductor $55440$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("en1")

sage: E.isogeny_class()

## Elliptic curves in class 55440.en

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55440.en1 55440ey2 $$[0, 0, 0, -4647, 121714]$$ $$59466754384/121275$$ $$22632825600$$ $$$$ $$61440$$ $$0.87338$$
55440.en2 55440ey1 $$[0, 0, 0, -192, 3211]$$ $$-67108864/343035$$ $$-4001160240$$ $$$$ $$30720$$ $$0.52680$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 55440.en have rank $$0$$.

## Complex multiplication

The elliptic curves in class 55440.en do not have complex multiplication.

## Modular form 55440.2.a.en

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} + q^{11} - 6q^{13} - 2q^{17} + O(q^{20})$$ ## 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 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. 