# Properties

 Label 42350.bl Number of curves 6 Conductor 42350 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("42350.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 42350.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42350.bl1 42350bb6 [1, 1, 0, -8259825, 9133575125]  1244160
42350.bl2 42350bb5 [1, 1, 0, -515825, 142791125]  622080
42350.bl3 42350bb4 [1, 1, 0, -107450, 11067500]  414720
42350.bl4 42350bb2 [1, 1, 0, -31825, -2197125]  138240
42350.bl5 42350bb1 [1, 1, 0, -1575, -49375]  69120 $$\Gamma_0(N)$$-optimal
42350.bl6 42350bb3 [1, 1, 0, 13550, 1024500]  207360

## Rank

sage: E.rank()

The elliptic curves in class 42350.bl have rank $$1$$.

## Modular form 42350.2.a.bl

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - 2q^{6} + q^{7} - q^{8} + q^{9} + 2q^{12} - 4q^{13} - q^{14} + q^{16} + 6q^{17} - q^{18} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 