# Properties

 Label 33600.cm Number of curves $2$ Conductor $33600$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cm1")

sage: E.isogeny_class()

## Elliptic curves in class 33600.cm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.cm1 33600ca2 $$[0, -1, 0, -22433, -1360863]$$ $$-7620530425/526848$$ $$-86318776320000$$ $$[]$$ $$124416$$ $$1.4250$$
33600.cm2 33600ca1 $$[0, -1, 0, 1567, -2463]$$ $$2595575/1512$$ $$-247726080000$$ $$[]$$ $$41472$$ $$0.87573$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 33600.cm have rank $$1$$.

## Complex multiplication

The elliptic curves in class 33600.cm do not have complex multiplication.

## Modular form 33600.2.a.cm

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} - 6q^{11} + q^{13} + 3q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.