Show commands:
SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 206310bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206310.bc3 | 206310bq1 | \([1, 0, 1, -9662112803, -376289031792994]\) | \(-673865164959526180786057849/23229524351662850520000\) | \(-3438803288445558705002312280000\) | \([2]\) | \(554729472\) | \(4.6327\) | \(\Gamma_0(N)\)-optimal |
| 206310.bc2 | 206310bq2 | \([1, 0, 1, -155850903083, -23681647502714482]\) | \(2828034254099032702891245115129/3196063848495740625000\) | \(473132153112828276135290625000\) | \([2]\) | \(1109458944\) | \(4.9792\) | |
| 206310.bc4 | 206310bq3 | \([1, 0, 1, 45818129662, -1313195780624812]\) | \(71856947906440606989120269591/46616317345728000000000000\) | \(-6900887980180964832192000000000000\) | \([2]\) | \(1664188416\) | \(5.1820\) | |
| 206310.bc1 | 206310bq4 | \([1, 0, 1, -195178358018, -10818675646294444]\) | \(5554585757634328021631979270889/2872902008056640625000000000\) | \(425292602772549957275390625000000000\) | \([2]\) | \(3328376832\) | \(5.5285\) |
Rank
sage: E.rank()
The elliptic curves in class 206310bq have rank \(1\).
Complex multiplication
The elliptic curves in class 206310bq do not have complex multiplication.Modular form 206310.2.a.bq
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
