# Properties

 Label 161700di Number of curves $2$ Conductor $161700$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("di1")

sage: E.isogeny_class()

## Elliptic curves in class 161700di

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.bo2 161700di1 $$[0, -1, 0, -26133, -5090238]$$ $$-67108864/343035$$ $$-10089431178750000$$ $$$$ $$1105920$$ $$1.7552$$ $$\Gamma_0(N)$$-optimal
161700.bo1 161700di2 $$[0, -1, 0, -632508, -193066488]$$ $$59466754384/121275$$ $$57071529900000000$$ $$$$ $$2211840$$ $$2.1017$$

## Rank

sage: E.rank()

The elliptic curves in class 161700di have rank $$0$$.

## Complex multiplication

The elliptic curves in class 161700di do not have complex multiplication.

## Modular form 161700.2.a.di

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + q^{11} - 6q^{13} + 2q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 