# Properties

 Label 2601.i Number of curves $2$ Conductor $2601$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 2601.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2601.i1 2601i1 [1, -1, 0, -207, -752]  768 $$\Gamma_0(N)$$-optimal
2601.i2 2601i2 [1, -1, 0, 558, -5495]  1536

## Rank

sage: E.rank()

The elliptic curves in class 2601.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2601.i do not have complex multiplication.

## Modular form2601.2.a.i

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 4q^{7} - 3q^{8} - 4q^{11} + 2q^{13} - 4q^{14} - q^{16} + 4q^{19} + O(q^{20})$$

## 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. 