# Properties

 Label 96600.i Number of curves $4$ Conductor $96600$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 96600.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96600.i1 96600b4 $$[0, -1, 0, -5520408, 4994188812]$$ $$581416486276209698/12425175$$ $$397605600000000$$ $$$$ $$1572864$$ $$2.3291$$
96600.i2 96600b2 $$[0, -1, 0, -345408, 77938812]$$ $$284840777767396/1312250625$$ $$20996010000000000$$ $$[2, 2]$$ $$786432$$ $$1.9825$$
96600.i3 96600b3 $$[0, -1, 0, -170408, 156688812]$$ $$-17101973157698/321306440175$$ $$-10281806085600000000$$ $$$$ $$1572864$$ $$2.3291$$
96600.i4 96600b1 $$[0, -1, 0, -32908, -186188]$$ $$985329269584/566015625$$ $$2264062500000000$$ $$$$ $$393216$$ $$1.6360$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 96600.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 96600.i do not have complex multiplication.

## Modular form 96600.2.a.i

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} - 2 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 