# Properties

 Label 97020.f Number of curves $4$ Conductor $97020$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 97020.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.f1 97020bk4 $$[0, 0, 0, -110248383, -445560267418]$$ $$6749703004355978704/5671875$$ $$124532407692000000$$ $$$$ $$4976640$$ $$3.0158$$
97020.f2 97020bk3 $$[0, 0, 0, -6889008, -6965095543]$$ $$-26348629355659264/24169921875$$ $$-33167367105468750000$$ $$$$ $$2488320$$ $$2.6692$$
97020.f3 97020bk2 $$[0, 0, 0, -1391943, -582034642]$$ $$13584145739344/1195803675$$ $$26255217326667436800$$ $$$$ $$1658880$$ $$2.4665$$
97020.f4 97020bk1 $$[0, 0, 0, 96432, -42349867]$$ $$72268906496/606436875$$ $$-832187814401790000$$ $$$$ $$829440$$ $$2.1199$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 97020.2.a.f

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 