# Properties

 Label 2736q Number of curves $3$ Conductor $2736$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 2736q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2736.c3 2736q1 $$[0, 0, 0, 96, -16]$$ $$32768/19$$ $$-56733696$$ $$[]$$ $$576$$ $$0.17728$$ $$\Gamma_0(N)$$-optimal
2736.c2 2736q2 $$[0, 0, 0, -1344, -20176]$$ $$-89915392/6859$$ $$-20480864256$$ $$[]$$ $$1728$$ $$0.72659$$
2736.c1 2736q3 $$[0, 0, 0, -110784, -14192656]$$ $$-50357871050752/19$$ $$-56733696$$ $$[]$$ $$5184$$ $$1.2759$$

## Rank

sage: E.rank()

The elliptic curves in class 2736q have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2736q do not have complex multiplication.

## Modular form2736.2.a.q

sage: E.q_eigenform(10)

$$q - 3q^{5} + q^{7} + 3q^{11} - 4q^{13} + 3q^{17} - q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 