# Properties

 Label 17424.bu Number of curves $6$ Conductor $17424$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("bu1")

sage: E.isogeny_class()

## Elliptic curves in class 17424.bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17424.bu1 17424t5 $$[0, 0, 0, -418539, 104219962]$$ $$3065617154/9$$ $$23804337604608$$ $$[2]$$ $$81920$$ $$1.7960$$
17424.bu2 17424t3 $$[0, 0, 0, -70059, -7136822]$$ $$28756228/3$$ $$3967389600768$$ $$[2]$$ $$40960$$ $$1.4495$$
17424.bu3 17424t4 $$[0, 0, 0, -26499, 1583890]$$ $$1556068/81$$ $$107119519220736$$ $$[2, 2]$$ $$40960$$ $$1.4495$$
17424.bu4 17424t2 $$[0, 0, 0, -4719, -93170]$$ $$35152/9$$ $$2975542200576$$ $$[2, 2]$$ $$20480$$ $$1.1029$$
17424.bu5 17424t1 $$[0, 0, 0, 726, -9317]$$ $$2048/3$$ $$-61990462512$$ $$[2]$$ $$10240$$ $$0.75633$$ $$\Gamma_0(N)$$-optimal
17424.bu6 17424t6 $$[0, 0, 0, 17061, 6279658]$$ $$207646/6561$$ $$-17353362113759232$$ $$[2]$$ $$81920$$ $$1.7960$$

## Rank

sage: E.rank()

The elliptic curves in class 17424.bu have rank $$1$$.

## Complex multiplication

The elliptic curves in class 17424.bu do not have complex multiplication.

## Modular form 17424.2.a.bu

sage: E.q_eigenform(10)

$$q + 2q^{5} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.