# Properties

 Label 247962l Number of curves $2$ Conductor $247962$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 247962l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.l1 247962l1 $$[1, 1, 0, -11403223, 12687986005]$$ $$6793805286030262681/1048227429629952$$ $$25301661910385610866688$$ $$$$ $$43352064$$ $$3.0222$$ $$\Gamma_0(N)$$-optimal
247962.l2 247962l2 $$[1, 1, 0, 19855017, 70046856405]$$ $$35862531227445945959/108547797844556928$$ $$-2620079960271044124028032$$ $$$$ $$86704128$$ $$3.3688$$

## Rank

sage: E.rank()

The elliptic curves in class 247962l have rank $$1$$.

## Complex multiplication

The elliptic curves in class 247962l do not have complex multiplication.

## Modular form 247962.2.a.l

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + 4q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} - 4q^{10} - q^{11} - q^{12} - q^{13} - 2q^{14} - 4q^{15} + q^{16} - q^{18} - 4q^{19} + O(q^{20})$$ ## 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. 