# Properties

 Label 46800.l Number of curves $2$ Conductor $46800$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 46800.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.l1 46800dl2 $$[0, 0, 0, -484275, -129734030]$$ $$-168256703745625/30371328$$ $$-2267207486668800$$ $$[]$$ $$373248$$ $$1.9502$$
46800.l2 46800dl1 $$[0, 0, 0, 1725, -594110]$$ $$7604375/2047032$$ $$-152810119987200$$ $$[]$$ $$124416$$ $$1.4009$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 46800.l have rank $$1$$.

## Complex multiplication

The elliptic curves in class 46800.l do not have complex multiplication.

## Modular form 46800.2.a.l

sage: E.q_eigenform(10)

$$q - 4q^{7} - q^{13} - 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.