# Properties

 Label 97020.m Number of curves $2$ Conductor $97020$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 97020.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.m1 97020bo2 $$[0, 0, 0, -227703, 41747902]$$ $$59466754384/121275$$ $$2662729299014400$$ $$$$ $$737280$$ $$1.8463$$
97020.m2 97020bo1 $$[0, 0, 0, -9408, 1101373]$$ $$-67108864/343035$$ $$-470732501075760$$ $$$$ $$368640$$ $$1.4998$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 97020.2.a.m

sage: E.q_eigenform(10)

$$q - q^{5} - q^{11} + 6q^{13} + 2q^{17} + O(q^{20})$$ ## 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. 