# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 46800.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.g1 46800bi2 $$[0, 0, 0, -13575, 553750]$$ $$94875856/9477$$ $$27634932000000$$ $$[2]$$ $$122880$$ $$1.3156$$
46800.g2 46800bi1 $$[0, 0, 0, 1050, 41875]$$ $$702464/4563$$ $$-831606750000$$ $$[2]$$ $$61440$$ $$0.96898$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 46800.2.a.g

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.