# Properties

 Label 46800eg Number of curves $2$ Conductor $46800$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("eg1")

sage: E.isogeny_class()

## Elliptic curves in class 46800eg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.v2 46800eg1 $$[0, 0, 0, -51163635, -154318995790]$$ $$-198417696411528597145/22989483914821632$$ $$-1716155778447868900147200$$ $$[]$$ $$6451200$$ $$3.3865$$ $$\Gamma_0(N)$$-optimal
46800.v1 46800eg2 $$[0, 0, 0, -32818501875, -2288369979868750]$$ $$-134057911417971280740025/1872$$ $$-54587520000000000$$ $$[]$$ $$32256000$$ $$4.1912$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 46800.2.a.eg

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.