# Properties

 Label 209300.i Number of curves $2$ Conductor $209300$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 209300.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
209300.i1 209300h2 $$[0, 0, 0, -8375, 24750]$$ $$16241202000/9332687$$ $$37330748000000$$ $$$$ $$414720$$ $$1.2939$$
209300.i2 209300h1 $$[0, 0, 0, -5500, -156375]$$ $$73598976000/336973$$ $$84243250000$$ $$$$ $$207360$$ $$0.94729$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 209300.i have rank $$1$$.

## Complex multiplication

The elliptic curves in class 209300.i do not have complex multiplication.

## Modular form 209300.2.a.i

sage: E.q_eigenform(10)

$$q + q^{7} - 3q^{9} + q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 