# Properties

 Label 100800.py Number of curves $2$ Conductor $100800$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("py1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.py

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.py1 100800il2 $$[0, 0, 0, -201900, 36945200]$$ $$-7620530425/526848$$ $$-62926387937280000$$ $$[]$$ $$995328$$ $$1.9743$$
100800.py2 100800il1 $$[0, 0, 0, 14100, 52400]$$ $$2595575/1512$$ $$-180592312320000$$ $$[]$$ $$331776$$ $$1.4250$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 100800.py have rank $$0$$.

## Complex multiplication

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

## Modular form 100800.2.a.py

sage: E.q_eigenform(10)

$$q + q^{7} + 6q^{11} + q^{13} - 3q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.