# Properties

 Label 97020.k Number of curves $2$ Conductor $97020$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 97020.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.k1 97020bm2 $$[0, 0, 0, -33663, 2357782]$$ $$192143824/1815$$ $$39850370461440$$ $$[2]$$ $$294912$$ $$1.4304$$
97020.k2 97020bm1 $$[0, 0, 0, -588, 88837]$$ $$-16384/2475$$ $$-3396338391600$$ $$[2]$$ $$147456$$ $$1.0839$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 97020.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 97020.k do not have complex multiplication.

## Modular form 97020.2.a.k

sage: E.q_eigenform(10)

$$q - q^{5} - q^{11} + 4q^{13} - 2q^{17} - 2q^{19} + O(q^{20})$$

## 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.