# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fa1")

sage: E.isogeny_class()

## Elliptic curves in class 93600fa

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.i2 93600fa1 $$[0, 0, 0, -1785, -29000]$$ $$107850176/117$$ $$682344000$$ $$[2]$$ $$57344$$ $$0.61068$$ $$\Gamma_0(N)$$-optimal
93600.i1 93600fa2 $$[0, 0, 0, -2235, -13250]$$ $$26463592/13689$$ $$638673984000$$ $$[2]$$ $$114688$$ $$0.95725$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 93600.2.a.fa

sage: E.q_eigenform(10)

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

## 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.