Properties

 Label 91b Number of curves 3 Conductor 91 CM no Rank 1 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("91.b1")
sage: E.isogeny_class()

Elliptic curves in class 91b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
91.b2 91b1 [0, 1, 1, -7, 5] 3 4 $$\Gamma_0(N)$$-optimal
91.b3 91b2 [0, 1, 1, 13, 42] 3 12
91.b1 91b3 [0, 1, 1, -117, -1245] 1 36

Rank

sage: E.rank()

The elliptic curves in class 91b have rank $$1$$.

Modular form91.2.a.b

sage: E.q_eigenform(10)
$$q - 2q^{3} - 2q^{4} - 3q^{5} + q^{7} + q^{9} + 4q^{12} + q^{13} + 6q^{15} + 4q^{16} - 6q^{17} - 7q^{19} + O(q^{20})$$

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. 