# Properties

 Label 1248j 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 1248j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1248.i2 1248j1 $$[0, 1, 0, -18, -36]$$ $$10648000/117$$ $$7488$$ $$$$ $$64$$ $$-0.44189$$ $$\Gamma_0(N)$$-optimal
1248.i1 1248j2 $$[0, 1, 0, -33, 15]$$ $$1000000/507$$ $$2076672$$ $$$$ $$128$$ $$-0.095314$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1248.2.a.j

sage: E.q_eigenform(10)

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

## 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 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. 