# Properties

 Label 1248.h Number of curves $2$ Conductor $1248$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 1248.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1248.h1 1248d2 $$[0, 1, 0, -1313, 17871]$$ $$61162984000/41067$$ $$168210432$$ $$$$ $$640$$ $$0.51681$$
1248.h2 1248d1 $$[0, 1, 0, -98, 132]$$ $$1643032000/767637$$ $$49128768$$ $$$$ $$320$$ $$0.17024$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1248.h have rank $$1$$.

## Complex multiplication

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

## Modular form1248.2.a.h

sage: E.q_eigenform(10)

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