# Properties

 Label 3600.z Number of curves $2$ Conductor $3600$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 3600.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.z1 3600bl2 $$[0, 0, 0, -273000, -54902500]$$ $$-30866268160/3$$ $$-218700000000$$ $$[]$$ $$17280$$ $$1.6092$$
3600.z2 3600bl1 $$[0, 0, 0, -3000, -92500]$$ $$-40960/27$$ $$-1968300000000$$ $$[]$$ $$5760$$ $$1.0599$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3600.z have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3600.z do not have complex multiplication.

## Modular form3600.2.a.z

sage: E.q_eigenform(10)

$$q + q^{7} + 6q^{11} + 5q^{13} + 6q^{17} - 5q^{19} + O(q^{20})$$ ## 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. 