# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 3744.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.c1 3744b2 $$[0, 0, 0, -1836, -30240]$$ $$8489664/13$$ $$1048080384$$ $$$$ $$1536$$ $$0.63042$$
3744.c2 3744b1 $$[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.c have rank $$0$$.

## Complex multiplication

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

## Modular form3744.2.a.c

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. 