# Properties

 Label 2800.h Number of curves $2$ Conductor $2800$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 2800.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.h1 2800z2 $$[0, -1, 0, -18208, 1334912]$$ $$-417267265/235298$$ $$-376476800000000$$ $$[]$$ $$8640$$ $$1.5000$$
2800.h2 2800z1 $$[0, -1, 0, 1792, -25088]$$ $$397535/392$$ $$-627200000000$$ $$[]$$ $$2880$$ $$0.95069$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2800.h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2800.h do not have complex multiplication.

## Modular form2800.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} - 2 q^{9} - 3 q^{11} + 2 q^{13} + 3 q^{17} + 7 q^{19} + O(q^{20})$$ ## 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. 