# Properties

 Label 405600p Number of curves $2$ Conductor $405600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 405600p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.p2 405600p1 $$[0, -1, 0, -2325158, 1190287812]$$ $$131096512/18225$$ $$193267001072925000000$$ $$$$ $$20127744$$ $$2.6190$$ $$\Gamma_0(N)$$-optimal
405600.p1 405600p2 $$[0, -1, 0, -9740033, -10502970063]$$ $$150568768/16875$$ $$11452859322840000000000$$ $$$$ $$40255488$$ $$2.9656$$

## Rank

sage: E.rank()

The elliptic curves in class 405600p have rank $$0$$.

## Complex multiplication

The elliptic curves in class 405600p do not have complex multiplication.

## Modular form 405600.2.a.p

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + 2q^{11} + 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 