# Properties

 Label 1288b Number of curves $2$ Conductor $1288$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1288b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1288.f2 1288b1 $$[0, -1, 0, -28, 84]$$ $$-9826000/3703$$ $$-947968$$ $$$$ $$160$$ $$-0.14333$$ $$\Gamma_0(N)$$-optimal
1288.f1 1288b2 $$[0, -1, 0, -488, 4316]$$ $$12576878500/1127$$ $$1154048$$ $$$$ $$320$$ $$0.20324$$

## Rank

sage: E.rank()

The elliptic curves in class 1288b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1288b do not have complex multiplication.

## Modular form1288.2.a.b

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{7} + q^{9} + 4q^{11} + 6q^{13} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 