# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 1248.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1248.e1 1248f1 $$[0, -1, 0, -2902, 61132]$$ $$42246001231552/14414517$$ $$922529088$$ $$$$ $$768$$ $$0.69180$$ $$\Gamma_0(N)$$-optimal
1248.e2 1248f2 $$[0, -1, 0, -2497, 78385]$$ $$-420526439488/390971529$$ $$-1601419382784$$ $$$$ $$1536$$ $$1.0384$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1248.2.a.e

sage: E.q_eigenform(10)

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