# Properties

 Label 900.b Number of curves $4$ Conductor $900$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 900.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
900.b1 900e3 $$[0, 0, 0, -9300, 345125]$$ $$488095744/125$$ $$22781250000$$ $$$$ $$864$$ $$0.97338$$
900.b2 900e4 $$[0, 0, 0, -8175, 431750]$$ $$-20720464/15625$$ $$-45562500000000$$ $$$$ $$1728$$ $$1.3200$$
900.b3 900e1 $$[0, 0, 0, -300, -1375]$$ $$16384/5$$ $$911250000$$ $$$$ $$288$$ $$0.42408$$ $$\Gamma_0(N)$$-optimal
900.b4 900e2 $$[0, 0, 0, 825, -9250]$$ $$21296/25$$ $$-72900000000$$ $$$$ $$576$$ $$0.77065$$

## Rank

sage: E.rank()

The elliptic curves in class 900.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 900.b do not have complex multiplication.

## Modular form900.2.a.b

sage: E.q_eigenform(10)

$$q - 2q^{7} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 