# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("rz1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.rz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.rz1 369600rz1 $$[0, 1, 0, -3008, -62262]$$ $$3010936384/121275$$ $$121275000000$$ $$$$ $$540672$$ $$0.89295$$ $$\Gamma_0(N)$$-optimal
369600.rz2 369600rz2 $$[0, 1, 0, 1367, -224137]$$ $$4410944/343035$$ $$-21954240000000$$ $$$$ $$1081344$$ $$1.2395$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 369600.2.a.rz

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} - q^{11} - 2 q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})$$

## 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. 