# Properties

 Label 248430ee Number of curves $6$ Conductor $248430$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("248430.ee1")

sage: E.isogeny_class()

## Elliptic curves in class 248430ee

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.ee6 248430ee1 [1, 0, 1, 124042, -6723832] [2] 4128768 $$\Gamma_0(N)$$-optimal
248430.ee5 248430ee2 [1, 0, 1, -538438, -56012344] [2, 2] 8257536
248430.ee3 248430ee3 [1, 0, 1, -4678938, 3855932056] [2, 2] 16515072
248430.ee2 248430ee4 [1, 0, 1, -6997618, -7119771592] [2] 16515072
248430.ee1 248430ee5 [1, 0, 1, -74653388, 248262691016] [2] 33030144
248430.ee4 248430ee6 [1, 0, 1, -952488, 9830176696] [2] 33030144

## Rank

sage: E.rank()

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

## Modular form 248430.2.a.ee

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} + q^{15} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.