# Properties

 Label 59248.n Number of curves $4$ Conductor $59248$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 59248.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
59248.n1 59248c4 [0, 0, 0, -158171, 24212330]  202752
59248.n2 59248c3 [0, 0, 0, -31211, -1679046]  202752
59248.n3 59248c2 [0, 0, 0, -10051, 365010] [2, 2] 101376
59248.n4 59248c1 [0, 0, 0, 529, 24334]  50688 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 59248.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 59248.n do not have complex multiplication.

## Modular form 59248.2.a.n

sage: E.q_eigenform(10)

$$q - 2q^{5} - q^{7} - 3q^{9} - 4q^{11} + 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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. 