# Properties

 Label 100800ft Number of curves $4$ Conductor $100800$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ft1")

sage: E.isogeny_class()

## Elliptic curves in class 100800ft

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.iv3 100800ft1 [0, 0, 0, -50700, 2774000] [2] 589824 $$\Gamma_0(N)$$-optimal
100800.iv2 100800ft2 [0, 0, 0, -338700, -73834000] [2, 2] 1179648
100800.iv4 100800ft3 [0, 0, 0, 93300, -249226000] [2] 2359296
100800.iv1 100800ft4 [0, 0, 0, -5378700, -4801354000] [2] 2359296

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 100800.2.a.ft

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.