# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 1248.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1248.j1 1248c1 $$[0, 1, 0, -2902, -61132]$$ $$42246001231552/14414517$$ $$922529088$$ $$$$ $$768$$ $$0.69180$$ $$\Gamma_0(N)$$-optimal
1248.j2 1248c2 $$[0, 1, 0, -2497, -78385]$$ $$-420526439488/390971529$$ $$-1601419382784$$ $$$$ $$1536$$ $$1.0384$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1248.2.a.j

sage: E.q_eigenform(10)

$$q + q^{3} + 2 q^{5} + 2 q^{7} + q^{9} - 2 q^{11} - q^{13} + 2 q^{15} + 6 q^{17} + 2 q^{19} + O(q^{20})$$

## 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. 