# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 97020.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.v1 97020bf2 $$[0, 0, 0, -562863, 220176502]$$ $$-18330740176/8857805$$ $$-9529671474123736320$$ $$$$ $$2177280$$ $$2.3473$$
97020.v2 97020bf1 $$[0, 0, 0, 54537, -3692738]$$ $$16674224/15125$$ $$-16272234605088000$$ $$[]$$ $$725760$$ $$1.7980$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 97020.2.a.v

sage: E.q_eigenform(10)

$$q - q^{5} + q^{11} - 4q^{13} - 6q^{17} + 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 