# Properties

 Label 48510.q Number of curves 4 Conductor 48510 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("48510.q1")

sage: E.isogeny_class()

## Elliptic curves in class 48510.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48510.q1 48510x4 [1, -1, 0, -14549040, 21363295050] [2] 2359296
48510.q2 48510x2 [1, -1, 0, -935370, 313838496] [2, 2] 1179648
48510.q3 48510x1 [1, -1, 0, -220950, -34655580] [2] 589824 $$\Gamma_0(N)$$-optimal
48510.q4 48510x3 [1, -1, 0, 1247580, 1559429766] [2] 2359296

## Rank

sage: E.rank()

The elliptic curves in class 48510.q have rank $$0$$.

## Modular form 48510.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + q^{11} - 2q^{13} + q^{16} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.