# Properties

 Label 100800mf Number of curves $4$ Conductor $100800$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("mf1")

sage: E.isogeny_class()

## Elliptic curves in class 100800mf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.bk3 100800mf1 $$[0, 0, 0, -8175, -142000]$$ $$82881856/36015$$ $$26254935000000$$ $$$$ $$294912$$ $$1.2710$$ $$\Gamma_0(N)$$-optimal
100800.bk2 100800mf2 $$[0, 0, 0, -63300, 6032000]$$ $$601211584/11025$$ $$514382400000000$$ $$[2, 2]$$ $$589824$$ $$1.6176$$
100800.bk4 100800mf3 $$[0, 0, 0, -300, 17498000]$$ $$-8/354375$$ $$-132269760000000000$$ $$$$ $$1179648$$ $$1.9642$$
100800.bk1 100800mf4 $$[0, 0, 0, -1008300, 389702000]$$ $$303735479048/105$$ $$39191040000000$$ $$$$ $$1179648$$ $$1.9642$$

## Rank

sage: E.rank()

The elliptic curves in class 100800mf have rank $$1$$.

## Complex multiplication

The elliptic curves in class 100800mf do not have complex multiplication.

## Modular form 100800.2.a.mf

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 