# Properties

 Label 46800el Number of curves $2$ Conductor $46800$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("el1")

sage: E.isogeny_class()

## Elliptic curves in class 46800el

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.j1 46800el1 $$[0, 0, 0, -3027675, -2027461750]$$ $$65787589563409/10400000$$ $$485222400000000000$$ $$$$ $$1105920$$ $$2.4041$$ $$\Gamma_0(N)$$-optimal
46800.j2 46800el2 $$[0, 0, 0, -2739675, -2428645750]$$ $$-48743122863889/26406250000$$ $$-1232010000000000000000$$ $$$$ $$2211840$$ $$2.7507$$

## Rank

sage: E.rank()

The elliptic curves in class 46800el have rank $$0$$.

## Complex multiplication

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

## Modular form 46800.2.a.el

sage: E.q_eigenform(10)

$$q - 4q^{7} - 2q^{11} + q^{13} + 2q^{17} - 6q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 