# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 3744.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.h1 3744n2 $$[0, 0, 0, -11820, -494336]$$ $$61162984000/41067$$ $$122625404928$$ $$$$ $$5120$$ $$1.0661$$
3744.h2 3744n1 $$[0, 0, 0, -885, -4448]$$ $$1643032000/767637$$ $$35814871872$$ $$$$ $$2560$$ $$0.71954$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3744.2.a.h

sage: E.q_eigenform(10)

$$q - 2q^{7} + 4q^{11} + q^{13} + 6q^{17} - 6q^{19} + O(q^{20})$$ ## 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 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. 