# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 97020.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.l1 97020a1 $$[0, 0, 0, -84040488, 296538415012]$$ $$-1647408715474378752/3025$$ $$-120535071148800$$ $$[3]$$ $$4499712$$ $$2.8484$$ $$\Gamma_0(N)$$-optimal
97020.l2 97020a2 $$[0, 0, 0, -83793528, 298367823348]$$ $$-2239956387422208/27680640625$$ $$-804066030629190252000000$$ $$[]$$ $$13499136$$ $$3.3977$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 97020.2.a.l

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.