# Properties

 Label 46200bl Number of curves $4$ Conductor $46200$ CM no Rank $0$ Graph

# Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 46200bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46200.de4 46200bl1 $$[0, 1, 0, 9092, 322688]$$ $$20777545136/23059575$$ $$-92238300000000$$ $$[2]$$ $$98304$$ $$1.3661$$ $$\Gamma_0(N)$$-optimal
46200.de3 46200bl2 $$[0, 1, 0, -51408, 2984688]$$ $$939083699236/300155625$$ $$4802490000000000$$ $$[2, 2]$$ $$196608$$ $$1.7127$$
46200.de2 46200bl3 $$[0, 1, 0, -326408, -69615312]$$ $$120186986927618/4332064275$$ $$138626056800000000$$ $$[2]$$ $$393216$$ $$2.0593$$
46200.de1 46200bl4 $$[0, 1, 0, -744408, 246920688]$$ $$1425631925916578/270703125$$ $$8662500000000000$$ $$[2]$$ $$393216$$ $$2.0593$$

## Rank

sage: E.rank()

The elliptic curves in class 46200bl have rank $$0$$.

## Complex multiplication

The elliptic curves in class 46200bl do not have complex multiplication.

## Modular form 46200.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + q^{11} + 2 q^{13} + 2 q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.