# Properties

 Label 23520.bl Number of curves $2$ Conductor $23520$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 23520.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23520.bl1 23520bt2 [0, 1, 0, -961, -11761]  16384
23520.bl2 23520bt1 [0, 1, 0, -86, -36]  8192 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 23520.bl have rank $$0$$.

## Complex multiplication

The elliptic curves in class 23520.bl do not have complex multiplication.

## Modular form 23520.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + 6q^{11} - 4q^{13} - q^{15} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 