# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 4368.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.e1 4368n2 $$[0, -1, 0, -58791936, 173529697152]$$ $$-5486773802537974663600129/2635437714$$ $$-10794752876544$$ $$[]$$ $$197568$$ $$2.7397$$
4368.e2 4368n1 $$[0, -1, 0, 11424, 5306112]$$ $$40251338884511/2997011332224$$ $$-12275758416789504$$ $$[]$$ $$28224$$ $$1.7667$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4368.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} - 5q^{11} - q^{13} + q^{15} - 3q^{17} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 