# Properties

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

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("48510.w1")

sage: E.isogeny_class()

## Elliptic curves in class 48510.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48510.w1 48510bb4 [1, -1, 0, -11517165, -14614939319] [2] 3981312
48510.w2 48510bb2 [1, -1, 0, -1577025, 755888125] [2] 1327104
48510.w3 48510bb1 [1, -1, 0, -24705, 29091901] [2] 663552 $$\Gamma_0(N)$$-optimal
48510.w4 48510bb3 [1, -1, 0, 222255, -783554675] [2] 1990656

## Rank

sage: E.rank()

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

## Modular form 48510.2.a.w

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.