Properties

 Label 148720.bq Number of curves 4 Conductor 148720 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("148720.bq1")

sage: E.isogeny_class()

Elliptic curves in class 148720.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
148720.bq1 148720bb4 [0, -1, 0, -1199956, 506336700] [2] 1866240
148720.bq2 148720bb3 [0, -1, 0, -75261, 7871876] [2] 933120
148720.bq3 148720bb2 [0, -1, 0, -16956, 485900] [2] 622080
148720.bq4 148720bb1 [0, -1, 0, -7661, -250264] [2] 311040 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 148720.bq have rank $$0$$.

Modular form 148720.2.a.bq

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} - 4q^{7} + q^{9} - q^{11} - 2q^{15} - 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.