# Properties

 Label 2646.q Number of curves $3$ Conductor $2646$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2646.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.q1 2646v3 $$[1, -1, 1, -62264, 5995567]$$ $$-11527859979/28$$ $$-64839187476$$ $$[]$$ $$10368$$ $$1.3149$$
2646.q2 2646v1 $$[1, -1, 1, -524, 13647]$$ $$-5000211/21952$$ $$-69731032896$$ $$[]$$ $$3456$$ $$0.76559$$ $$\Gamma_0(N)$$-optimal
2646.q3 2646v2 $$[1, -1, 1, 4621, -327981]$$ $$381790581/1835008$$ $$-52460506054656$$ $$[]$$ $$10368$$ $$1.3149$$

## Rank

sage: E.rank()

The elliptic curves in class 2646.q have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2646.q do not have complex multiplication.

## Modular form2646.2.a.q

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - 3q^{5} + q^{8} - 3q^{10} - 3q^{11} + 4q^{13} + q^{16} - 6q^{17} + 7q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 