# Properties

 Label 9900.bd Number of curves $4$ Conductor $9900$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 9900.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9900.bd1 9900t4 [0, 0, 0, -1597575, 777212750] [2] 124416
9900.bd2 9900t3 [0, 0, 0, -100200, 12054125] [2] 62208
9900.bd3 9900t2 [0, 0, 0, -22575, 737750] [2] 41472
9900.bd4 9900t1 [0, 0, 0, -10200, -388375] [2] 20736 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 9900.bd have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9900.bd do not have complex multiplication.

## Modular form9900.2.a.bd

sage: E.q_eigenform(10)

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

## 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.