# Properties

 Label 1248b Number of curves $2$ Conductor $1248$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1248b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1248.d2 1248b1 $$[0, -1, 0, -98, -132]$$ $$1643032000/767637$$ $$49128768$$ $$$$ $$320$$ $$0.17024$$ $$\Gamma_0(N)$$-optimal
1248.d1 1248b2 $$[0, -1, 0, -1313, -17871]$$ $$61162984000/41067$$ $$168210432$$ $$$$ $$640$$ $$0.51681$$

## Rank

sage: E.rank()

The elliptic curves in class 1248b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1248b do not have complex multiplication.

## Modular form1248.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{7} + q^{9} + 4 q^{11} + q^{13} - 6 q^{17} + 6 q^{19} + O(q^{20})$$

## 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 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. 