# Properties

 Label 248430j Number of curves $2$ Conductor $248430$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("248430.j1")

sage: E.isogeny_class()

## Elliptic curves in class 248430j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.j1 248430j1 [1, 1, 0, -2538, -19872]  442368 $$\Gamma_0(N)$$-optimal
248430.j2 248430j2 [1, 1, 0, 9292, -140538]  884736

## Rank

sage: E.rank()

The elliptic curves in class 248430j have rank $$2$$.

## Modular form 248430.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - 2q^{11} - q^{12} + q^{15} + q^{16} - 4q^{17} - q^{18} + O(q^{20})$$

## 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. 