# Properties

 Label 144150.ca Number of curves $6$ Conductor $144150$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("144150.ca1")

sage: E.isogeny_class()

## Elliptic curves in class 144150.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
144150.ca1 144150dn5 [1, 0, 1, -7388168501, 244428705244148] [2] 94371840
144150.ca2 144150dn3 [1, 0, 1, -461761001, 3819161509148] [2, 2] 47185920
144150.ca3 144150dn6 [1, 0, 1, -454553501, 3944153974148] [2] 94371840
144150.ca4 144150dn4 [1, 0, 1, -88893001, -251519170852] [2] 47185920
144150.ca5 144150dn2 [1, 0, 1, -29311001, 57711409148] [2, 2] 23592960
144150.ca6 144150dn1 [1, 0, 1, 1440999, 3772401148] [2] 11796480 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 144150.ca have rank $$1$$.

## Modular form 144150.2.a.ca

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 4q^{11} + q^{12} + 6q^{13} + q^{16} + 2q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.