# Properties

 Label 144.b Number of curves $6$ Conductor $144$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 144.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
144.b1 144b5 $$[0, 0, 0, -3459, -78302]$$ $$3065617154/9$$ $$13436928$$ $$$$ $$64$$ $$0.59710$$
144.b2 144b4 $$[0, 0, 0, -579, 5362]$$ $$28756228/3$$ $$2239488$$ $$$$ $$32$$ $$0.25053$$
144.b3 144b3 $$[0, 0, 0, -219, -1190]$$ $$1556068/81$$ $$60466176$$ $$[2, 2]$$ $$32$$ $$0.25053$$
144.b4 144b2 $$[0, 0, 0, -39, 70]$$ $$35152/9$$ $$1679616$$ $$[2, 2]$$ $$16$$ $$-0.096046$$
144.b5 144b1 $$[0, 0, 0, 6, 7]$$ $$2048/3$$ $$-34992$$ $$$$ $$8$$ $$-0.44262$$ $$\Gamma_0(N)$$-optimal
144.b6 144b6 $$[0, 0, 0, 141, -4718]$$ $$207646/6561$$ $$-9795520512$$ $$$$ $$64$$ $$0.59710$$

## Rank

sage: E.rank()

The elliptic curves in class 144.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 144.b do not have complex multiplication.

## Modular form144.2.a.b

sage: E.q_eigenform(10)

$$q + 2 q^{5} + 4 q^{11} - 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 