# Properties

 Label 345520.bn Number of curves 2 Conductor 345520 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("345520.bn1")

sage: E.isogeny_class()

## Elliptic curves in class 345520.bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
345520.bn1 345520bn2 [0, 0, 0, -20332507, 154395929354] [] 146595456
345520.bn2 345520bn1 [0, 0, 0, -2205307, -1279493206] [] 20942208 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 345520.bn have rank $$0$$.

## Modular form 345520.2.a.bn

sage: E.q_eigenform(10)

$$q + 3q^{3} + q^{5} - q^{7} + 6q^{9} + 2q^{11} - 7q^{13} + 3q^{15} + 4q^{17} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 