# Properties

 Label 8034.i Number of curves 2 Conductor 8034 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8034.i1")

sage: E.isogeny_class()

## Elliptic curves in class 8034.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8034.i1 8034i2 [1, 0, 0, -258, -1584]  2304
8034.i2 8034i1 [1, 0, 0, 2, -76]  1152 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8034.i have rank $$0$$.

## Modular form8034.2.a.i

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + 2q^{11} + q^{12} + q^{13} + q^{16} - 2q^{17} + q^{18} + 8q^{19} + O(q^{20})$$

## 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. 