# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 3744.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.d1 3744l1 $$[0, 0, 0, -26121, 1624444]$$ $$42246001231552/14414517$$ $$672523705152$$ $$$$ $$6144$$ $$1.2411$$ $$\Gamma_0(N)$$-optimal
3744.d2 3744l2 $$[0, 0, 0, -22476, 2093920]$$ $$-420526439488/390971529$$ $$-1167434730049536$$ $$$$ $$12288$$ $$1.5877$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3744.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{5} + 2q^{7} + 2q^{11} - q^{13} - 6q^{17} + 2q^{19} + O(q^{20})$$ ## 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. 