# Properties

 Label 97461.k Number of curves $2$ Conductor $97461$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 97461.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.k1 97461i1 $$[1, -1, 1, -20075, 1033386]$$ $$10431681625/710073$$ $$60900206836833$$ $$$$ $$294912$$ $$1.3935$$ $$\Gamma_0(N)$$-optimal
97461.k2 97461i2 $$[1, -1, 1, 17410, 4422030]$$ $$6804992375/102626433$$ $$-8801871070476393$$ $$$$ $$589824$$ $$1.7401$$

## Rank

sage: E.rank()

The elliptic curves in class 97461.k have rank $$1$$.

## Complex multiplication

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

## Modular form 97461.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 3q^{8} - 4q^{11} - q^{13} - q^{16} - q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 