# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("3520.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 3520g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3520.bd4 3520g1 [0, -1, 0, -181, 981]  1152 $$\Gamma_0(N)$$-optimal
3520.bd3 3520g2 [0, -1, 0, -401, -1615]  2304
3520.bd2 3520g3 [0, -1, 0, -1781, -27979]  3456
3520.bd1 3520g4 [0, -1, 0, -28401, -1832815]  6912

## Rank

sage: E.rank()

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

## Modular form3520.2.a.bd

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 Cremona 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 Cremona labels. 