# Properties

 Label 100800pd Number of curves $2$ Conductor $100800$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("pd1")

sage: E.isogeny_class()

## Elliptic curves in class 100800pd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.d2 100800pd1 $$[0, 0, 0, 14100, -52400]$$ $$2595575/1512$$ $$-180592312320000$$ $$[]$$ $$331776$$ $$1.4250$$ $$\Gamma_0(N)$$-optimal
100800.d1 100800pd2 $$[0, 0, 0, -201900, -36945200]$$ $$-7620530425/526848$$ $$-62926387937280000$$ $$[]$$ $$995328$$ $$1.9743$$

## Rank

sage: E.rank()

The elliptic curves in class 100800pd have rank $$2$$.

## Complex multiplication

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

## Modular form 100800.2.a.pd

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 Cremona 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 Cremona labels. 