# Properties

 Label 3520.d Number of curves 4 Conductor 3520 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3520.d1")

sage: E.isogeny_class()

## Elliptic curves in class 3520.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3520.d1 3520u4 [0, 1, 0, -28401, 1832815]  6912
3520.d2 3520u3 [0, 1, 0, -1781, 27979]  3456
3520.d3 3520u2 [0, 1, 0, -401, 1615]  2304
3520.d4 3520u1 [0, 1, 0, -181, -981]  1152 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3520.d have rank $$0$$.

## Modular form3520.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} + 4q^{7} + q^{9} - q^{11} + 4q^{13} + 2q^{15} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 