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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 255024.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 255024.bq1 | 255024bq3 | \([0, 0, 0, -1380364131, 19739587369570]\) | \(97413070452067229637409633/140666577176907936\) | \(420028148785012266369024\) | \([2]\) | \(70778880\) | \(3.8036\) | |
| 255024.bq2 | 255024bq4 | \([0, 0, 0, -221129571, -853888563614]\) | \(400476194988122984445793/126270124548858769248\) | \(377040571580899503234220032\) | \([2]\) | \(70778880\) | \(3.8036\) | |
| 255024.bq3 | 255024bq2 | \([0, 0, 0, -87059811, 302516744290]\) | \(24439335640029940889953/902916953746891776\) | \(2696095577216958892867584\) | \([2, 2]\) | \(35389440\) | \(3.4570\) | |
| 255024.bq4 | 255024bq1 | \([0, 0, 0, 2151069, 16881348706]\) | \(368637286278891167/41443067603976192\) | \(-123748336776391245692928\) | \([2]\) | \(17694720\) | \(3.1104\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 255024.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 255024.bq do not have complex multiplication.Modular form 255024.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
