# Properties

 Label 248430.iz Number of curves $4$ Conductor $248430$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("iz1")

sage: E.isogeny_class()

## Elliptic curves in class 248430.iz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.iz1 248430iz4 [1, 0, 0, -3093126, -2094101010]  7077888
248430.iz2 248430iz2 [1, 0, 0, -194776, -32214820] [2, 2] 3538944
248430.iz3 248430iz1 [1, 0, 0, -29156, 1207296]  1769472 $$\Gamma_0(N)$$-optimal
248430.iz4 248430iz3 [1, 0, 0, 53654, -108681574]  7077888

## Rank

sage: E.rank()

The elliptic curves in class 248430.iz have rank $$0$$.

## Complex multiplication

The elliptic curves in class 248430.iz do not have complex multiplication.

## Modular form 248430.2.a.iz

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 