Properties

 Label 88935.bq Number of curves $6$ Conductor $88935$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bq1")

sage: E.isogeny_class()

Elliptic curves in class 88935.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88935.bq1 88935m6 [1, 1, 0, -18078706923, -935626807637892] [2] 44236800
88935.bq2 88935m4 [1, 1, 0, -1129919298, -14619518822817] [2, 2] 22118400
88935.bq3 88935m5 [1, 1, 0, -1124316393, -14771672431578] [2] 44236800
88935.bq4 88935m3 [1, 1, 0, -150863528, 376052042997] [2] 22118400
88935.bq5 88935m2 [1, 1, 0, -70970253, -226071613368] [2, 2] 11059200
88935.bq6 88935m1 [1, 1, 0, 207392, -10559939837] [2] 5529600 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 88935.bq have rank $$1$$.

Complex multiplication

The elliptic curves in class 88935.bq do not have complex multiplication.

Modular form 88935.2.a.bq

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - 3q^{8} + q^{9} - q^{10} + q^{12} - 2q^{13} + q^{15} - q^{16} + 2q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.