# Properties

 Label 97461.l Number of curves $2$ Conductor $97461$ CM no Rank $0$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 97461.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.l1 97461d2 $$[1, -1, 1, -26984, 658928]$$ $$684030715731/338005577$$ $$1073682489468771$$ $$$$ $$368640$$ $$1.5772$$
97461.l2 97461d1 $$[1, -1, 1, -14489, -660544]$$ $$105890949891/1288651$$ $$4093429540473$$ $$$$ $$184320$$ $$1.2307$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 97461.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 97461.l do not have complex multiplication.

## Modular form 97461.2.a.l

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 2q^{5} + 3q^{8} - 2q^{10} + q^{13} - q^{16} + q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 