# Properties

 Label 3744.n Number of curves $2$ Conductor $3744$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 3744.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.n1 3744a2 $$[0, 0, 0, -204, -1120]$$ $$8489664/13$$ $$1437696$$ $$$$ $$512$$ $$0.081110$$
3744.n2 3744a1 $$[0, 0, 0, -9, -28]$$ $$-46656/169$$ $$-292032$$ $$$$ $$256$$ $$-0.26546$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3744.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3744.n do not have complex multiplication.

## Modular form3744.2.a.n

sage: E.q_eigenform(10)

$$q + 2q^{5} + 2q^{11} + q^{13} + 4q^{19} + O(q^{20})$$ ## 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 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. 