# Properties

 Label 142800dm Number of curves $6$ Conductor $142800$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("142800.ct1")

sage: E.isogeny_class()

## Elliptic curves in class 142800dm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
142800.ct5 142800dm1 [0, -1, 0, -28097608, -57244982288] [2] 11796480 $$\Gamma_0(N)$$-optimal
142800.ct4 142800dm2 [0, -1, 0, -36289608, -21134646288] [2, 2] 23592960
142800.ct2 142800dm3 [0, -1, 0, -343617608, 2435030729712] [2, 2] 47185920
142800.ct6 142800dm4 [0, -1, 0, 139966392, -166369590288] [2] 47185920
142800.ct1 142800dm5 [0, -1, 0, -5487441608, 156461696585712] [2] 94371840
142800.ct3 142800dm6 [0, -1, 0, -117041608, 5598031689712] [2] 94371840

## Rank

sage: E.rank()

The elliptic curves in class 142800dm have rank $$1$$.

## Modular form 142800.2.a.ct

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} - 4q^{11} + 2q^{13} - q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.