# Properties

 Label 3600.bd Number of curves $2$ Conductor $3600$ CM no Rank $1$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

## Elliptic curves in class 3600.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.bd1 3600d2 $$[0, 0, 0, -3075, 65250]$$ $$3721734/25$$ $$21600000000$$ $$$$ $$3072$$ $$0.81771$$
3600.bd2 3600d1 $$[0, 0, 0, -75, 2250]$$ $$-108/5$$ $$-2160000000$$ $$$$ $$1536$$ $$0.47114$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3600.bd have rank $$1$$.

## Complex multiplication

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

## Modular form3600.2.a.bd

sage: E.q_eigenform(10)

$$q + 2q^{7} - 2q^{11} - 4q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 