# Properties

 Label 3300.b Number of curves $4$ Conductor $3300$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 3300.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3300.b1 3300e4 $$[0, -1, 0, -6249908, -6011849688]$$ $$6749703004355978704/5671875$$ $$22687500000000$$ $$$$ $$41472$$ $$2.2983$$
3300.b2 3300e3 $$[0, -1, 0, -390533, -93880938]$$ $$-26348629355659264/24169921875$$ $$-6042480468750000$$ $$$$ $$20736$$ $$1.9517$$
3300.b3 3300e2 $$[0, -1, 0, -78908, -7829688]$$ $$13584145739344/1195803675$$ $$4783214700000000$$ $$$$ $$13824$$ $$1.7490$$
3300.b4 3300e1 $$[0, -1, 0, 5467, -573438]$$ $$72268906496/606436875$$ $$-151609218750000$$ $$$$ $$6912$$ $$1.4024$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3300.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3300.b do not have complex multiplication.

## Modular form3300.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} + q^{11} - 2q^{13} + 2q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 