# Properties

 Label 13520bb Number of curves 4 Conductor 13520 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("13520.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 13520bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13520.bc3 13520bb1 [0, -1, 0, -225, -820]  4608 $$\Gamma_0(N)$$-optimal
13520.bc4 13520bb2 [0, -1, 0, 620, -6228]  9216
13520.bc1 13520bb3 [0, -1, 0, -6985, 226992]  13824
13520.bc2 13520bb4 [0, -1, 0, -6140, 283100]  27648

## Rank

sage: E.rank()

The elliptic curves in class 13520bb have rank $$1$$.

## Modular form 13520.2.a.bc

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{15} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 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. 