# Properties

 Label 93600z Number of curves $2$ Conductor $93600$ CM no Rank $2$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 93600z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.bf2 93600z1 $$[0, 0, 0, -15825, -1271000]$$ $$-601211584/609375$$ $$-444234375000000$$ $$[2]$$ $$368640$$ $$1.5062$$ $$\Gamma_0(N)$$-optimal
93600.bf1 93600z2 $$[0, 0, 0, -297075, -62302250]$$ $$497169541448/190125$$ $$1108809000000000$$ $$[2]$$ $$737280$$ $$1.8528$$

## Rank

sage: E.rank()

The elliptic curves in class 93600z have rank $$2$$.

## Complex multiplication

The elliptic curves in class 93600z do not have complex multiplication.

## Modular form 93600.2.a.z

sage: E.q_eigenform(10)

$$q - 2q^{7} - 4q^{11} - q^{13} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.