# Properties

 Label 248430.ec Number of curves $6$ Conductor $248430$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("248430.ec1")

sage: E.isogeny_class()

## Elliptic curves in class 248430.ec

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.ec1 248430ec5 [1, 0, 1, -139120973, 631580989106] [2] 28311552
248430.ec2 248430ec3 [1, 0, 1, -8695223, 9867524006] [2, 2] 14155776
248430.ec3 248430ec6 [1, 0, 1, -8115553, 11239950698] [2] 28311552
248430.ec4 248430ec4 [1, 0, 1, -3064143, -1951516682] [2] 14155776
248430.ec5 248430ec2 [1, 0, 1, -579843, 132314158] [2, 2] 7077888
248430.ec6 248430ec1 [1, 0, 1, 82637, 12802766] [2] 3538944 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 248430.2.a.ec

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.