# Properties

 Label 97461.x Number of curves $2$ Conductor $97461$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 97461.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.x1 97461c1 $$[1, -1, 0, -2293650, -1336276537]$$ $$420100556152674123/62939003491$$ $$199927192186241793$$ $$$$ $$2211840$$ $$2.3330$$ $$\Gamma_0(N)$$-optimal
97461.x2 97461c2 $$[1, -1, 0, -2081235, -1593935932]$$ $$-313859434290315003/164114213839849$$ $$-521312574889198665027$$ $$$$ $$4423680$$ $$2.6796$$

## Rank

sage: E.rank()

The elliptic curves in class 97461.x have rank $$0$$.

## Complex multiplication

The elliptic curves in class 97461.x do not have complex multiplication.

## Modular form 97461.2.a.x

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + 4q^{5} - 3q^{8} + 4q^{10} + q^{13} - q^{16} + q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 