# Properties

 Label 97461.p Number of curves $2$ Conductor $97461$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 97461.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.p1 97461n1 $$[1, -1, 0, -200664, 34629979]$$ $$10418796526321/6390657$$ $$548101861531497$$ $$[2]$$ $$860160$$ $$1.7709$$ $$\Gamma_0(N)$$-optimal
97461.p2 97461n2 $$[1, -1, 0, -163179, 47937154]$$ $$-5602762882081/8312741073$$ $$-712951556708587833$$ $$[2]$$ $$1720320$$ $$2.1175$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 97461.2.a.p

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 4q^{5} - 3q^{8} - 4q^{10} + 4q^{11} - q^{13} - q^{16} + q^{17} + O(q^{20})$$

## 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.