# Properties

 Label 91035.ba Number of curves $3$ Conductor $91035$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 91035.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.ba1 91035d3 $$[0, 0, 1, -341598, 80387734]$$ $$-250523582464/13671875$$ $$-240574247279296875$$ $$[]$$ $$907200$$ $$2.0934$$
91035.ba2 91035d1 $$[0, 0, 1, -3468, -87206]$$ $$-262144/35$$ $$-615870073035$$ $$[]$$ $$100800$$ $$0.99476$$ $$\Gamma_0(N)$$-optimal
91035.ba3 91035d2 $$[0, 0, 1, 22542, 222313]$$ $$71991296/42875$$ $$-754440839467875$$ $$[]$$ $$302400$$ $$1.5441$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 91035.ba do not have complex multiplication.

## Modular form 91035.2.a.ba

sage: E.q_eigenform(10)

$$q - 2q^{4} - q^{5} - q^{7} - 3q^{11} + 5q^{13} + 4q^{16} + 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 