# Properties

 Label 3600.d Number of curves $2$ Conductor $3600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 3600.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.d1 3600br1 $$[0, 0, 0, -3000, 59375]$$ $$131072/9$$ $$205031250000$$ $$[2]$$ $$3840$$ $$0.91877$$ $$\Gamma_0(N)$$-optimal
3600.d2 3600br2 $$[0, 0, 0, 2625, 256250]$$ $$5488/81$$ $$-29524500000000$$ $$[2]$$ $$7680$$ $$1.2653$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3600.2.a.d

sage: E.q_eigenform(10)

$$q - 4q^{7} - 4q^{11} - 4q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.