# Properties

 Label 1440.b Number of curves $2$ Conductor $1440$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1440.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1440.b1 1440a2 $$[0, 0, 0, -243, -1242]$$ $$157464/25$$ $$251942400$$ $$$$ $$384$$ $$0.33467$$
1440.b2 1440a1 $$[0, 0, 0, 27, -108]$$ $$1728/5$$ $$-6298560$$ $$$$ $$192$$ $$-0.011906$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1440.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1440.b do not have complex multiplication.

## Modular form1440.2.a.b

sage: E.q_eigenform(10)

$$q - q^{5} - 2 q^{7} + 2 q^{11} + 2 q^{17} - 4 q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 