# Properties

 Label 97461.m Number of curves $2$ Conductor $97461$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 97461.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97461.m1 97461x1 $$[1, -1, 1, -26249, 1643240]$$ $$23320116793/2873$$ $$246406065633$$ $$[2]$$ $$207360$$ $$1.2092$$ $$\Gamma_0(N)$$-optimal
97461.m2 97461x2 $$[1, -1, 1, -24044, 1929008]$$ $$-17923019113/8254129$$ $$-707924626563609$$ $$[2]$$ $$414720$$ $$1.5558$$

## Rank

sage: E.rank()

The elliptic curves in class 97461.m have rank $$1$$.

## Complex multiplication

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

## Modular form 97461.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 2q^{5} + 3q^{8} - 2q^{10} + 6q^{11} + q^{13} - q^{16} + q^{17} - 4q^{19} + O(q^{20})$$

## 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.