# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bt1")

sage: E.isogeny_class()

## Elliptic curves in class 46800bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.i2 46800bt1 $$[0, 0, 0, -315, -1350]$$ $$37044/13$$ $$1213056000$$ $$$$ $$20480$$ $$0.44439$$ $$\Gamma_0(N)$$-optimal
46800.i1 46800bt2 $$[0, 0, 0, -2115, 36450]$$ $$5606442/169$$ $$31539456000$$ $$$$ $$40960$$ $$0.79096$$

## Rank

sage: E.rank()

The elliptic curves in class 46800bt have rank $$2$$.

## Complex multiplication

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

## Modular form 46800.2.a.bt

sage: E.q_eigenform(10)

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