# Properties

 Label 66248.p Number of curves $4$ Conductor $66248$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 66248.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
66248.p1 66248e4 [0, 0, 0, -2476019, -1499606290] [2] 884736
66248.p2 66248e3 [0, 0, 0, -488579, 103992798] [2] 884736
66248.p3 66248e2 [0, 0, 0, -157339, -22607130] [2, 2] 442368
66248.p4 66248e1 [0, 0, 0, 8281, -1507142] [2] 221184 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 66248.p have rank $$0$$.

## Complex multiplication

The elliptic curves in class 66248.p do not have complex multiplication.

## Modular form 66248.2.a.p

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.