# Properties

 Label 3744.b Number of curves $2$ Conductor $3744$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 3744.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.b1 3744j2 $$[0, 0, 0, -1836, 30240]$$ $$8489664/13$$ $$1048080384$$ $$$$ $$1536$$ $$0.63042$$
3744.b2 3744j1 $$[0, 0, 0, -81, 756]$$ $$-46656/169$$ $$-212891328$$ $$$$ $$768$$ $$0.28384$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3744.b have rank $$1$$.

## Complex multiplication

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

## Modular form3744.2.a.b

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. 