# Properties

 Label 369600.ra Number of curves $2$ Conductor $369600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ra1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.ra

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.ra1 369600ra2 $$[0, 1, 0, -1812833, -939813537]$$ $$10294787169064/3361743$$ $$215151552000000000$$ $$$$ $$5898240$$ $$2.2996$$
369600.ra2 369600ra1 $$[0, 1, 0, -97833, -18858537]$$ $$-12944768192/11647251$$ $$-93178008000000000$$ $$$$ $$2949120$$ $$1.9530$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 369600.ra have rank $$0$$.

## Complex multiplication

The elliptic curves in class 369600.ra do not have complex multiplication.

## Modular form 369600.2.a.ra

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} - q^{11} - 6 q^{13} + 2 q^{17} + 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 