# Properties

 Label 4368.g Number of curves $2$ Conductor $4368$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("g1")

E.isogeny_class()

## Elliptic curves in class 4368.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.g1 4368e2 $$[0, -1, 0, -2668, 32656]$$ $$8207369602000/3046751253$$ $$779968320768$$ $$$$ $$3584$$ $$0.98183$$
4368.g2 4368e1 $$[0, -1, 0, 517, 3354]$$ $$953312000000/887416803$$ $$-14198668848$$ $$$$ $$1792$$ $$0.63526$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4368.g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4368.g do not have complex multiplication.

## Modular form4368.2.a.g

sage: E.q_eigenform(10)

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

## 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 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. 