# Properties

 Label 91035.bi Number of curves 4 Conductor 91035 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("91035.bi1")

sage: E.isogeny_class()

## Elliptic curves in class 91035.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91035.bi1 91035h4 [1, -1, 0, -4385340, -3533456039]  2359296
91035.bi2 91035h3 [1, -1, 0, -1394190, 589363051]  2359296
91035.bi3 91035h2 [1, -1, 0, -288765, -48909344] [2, 2] 1179648
91035.bi4 91035h1 [1, -1, 0, 36360, -4497269]  589824 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 91035.bi have rank $$0$$.

## Modular form 91035.2.a.bi

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - q^{5} - q^{7} - 3q^{8} - q^{10} - 6q^{13} - q^{14} - q^{16} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 