# Properties

 Label 217672k Number of curves $2$ Conductor $217672$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 217672k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
217672.r2 217672k1 $$[0, -1, 0, -4788, 165476]$$ $$-9826000/3703$$ $$-4575660474112$$ $$$$ $$307200$$ $$1.1391$$ $$\Gamma_0(N)$$-optimal
217672.r1 217672k2 $$[0, -1, 0, -82528, 9152220]$$ $$12576878500/1127$$ $$5570369272832$$ $$$$ $$614400$$ $$1.4857$$

## Rank

sage: E.rank()

The elliptic curves in class 217672k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 217672k do not have complex multiplication.

## Modular form 217672.2.a.k

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{7} + q^{9} - 4q^{11} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 