# Properties

 Label 900e Number of curves 4 Conductor 900 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("900.b1")

sage: E.isogeny_class()

## Elliptic curves in class 900e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
900.b3 900e1 [0, 0, 0, -300, -1375]  288 $$\Gamma_0(N)$$-optimal
900.b4 900e2 [0, 0, 0, 825, -9250]  576
900.b1 900e3 [0, 0, 0, -9300, 345125]  864
900.b2 900e4 [0, 0, 0, -8175, 431750]  1728

## Rank

sage: E.rank()

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

## 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 Cremona 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 Cremona labels. 