# Properties

 Label 11592l Number of curves $2$ Conductor $11592$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 11592l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11592.j2 11592l1 $$[0, 0, 0, -255, -2014]$$ $$-9826000/3703$$ $$-691068672$$ $$$$ $$3840$$ $$0.40598$$ $$\Gamma_0(N)$$-optimal
11592.j1 11592l2 $$[0, 0, 0, -4395, -112138]$$ $$12576878500/1127$$ $$841300992$$ $$$$ $$7680$$ $$0.75255$$

## Rank

sage: E.rank()

The elliptic curves in class 11592l have rank $$1$$.

## Complex multiplication

The elliptic curves in class 11592l do not have complex multiplication.

## Modular form 11592.2.a.l

sage: E.q_eigenform(10)

$$q - q^{7} - 4q^{11} + 6q^{13} + O(q^{20})$$ ## 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. 