# Properties

 Label 931b Number of curves $3$ Conductor $931$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 931b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
931.a3 931b1 $$[0, -1, 1, 33, -8]$$ $$32768/19$$ $$-2235331$$ $$[]$$ $$126$$ $$-0.092218$$ $$\Gamma_0(N)$$-optimal
931.a2 931b2 $$[0, -1, 1, -457, 4157]$$ $$-89915392/6859$$ $$-806954491$$ $$[]$$ $$378$$ $$0.45709$$
931.a1 931b3 $$[0, -1, 1, -37697, 2829742]$$ $$-50357871050752/19$$ $$-2235331$$ $$[]$$ $$1134$$ $$1.0064$$

## Rank

sage: E.rank()

The elliptic curves in class 931b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 931b do not have complex multiplication.

## Modular form931.2.a.b

sage: E.q_eigenform(10)

$$q + 2q^{3} - 2q^{4} - 3q^{5} + q^{9} + 3q^{11} - 4q^{12} + 4q^{13} - 6q^{15} + 4q^{16} + 3q^{17} - q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 