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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 24150bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24150.bl3 | 24150bn1 | \([1, 1, 1, -5505063, 4969250781]\) | \(1180838681727016392361/692428800000\) | \(10819200000000000\) | \([4]\) | \(737280\) | \(2.4008\) | \(\Gamma_0(N)\)-optimal |
| 24150.bl2 | 24150bn2 | \([1, 1, 1, -5537063, 4908514781]\) | \(1201550658189465626281/28577902500000000\) | \(446529726562500000000\) | \([2, 2]\) | \(1474560\) | \(2.7474\) | |
| 24150.bl4 | 24150bn3 | \([1, 1, 1, 712937, 15371014781]\) | \(2564821295690373719/6533572090396050000\) | \(-102087063912438281250000\) | \([2]\) | \(2949120\) | \(3.0940\) | |
| 24150.bl1 | 24150bn4 | \([1, 1, 1, -12299063, -9440449219]\) | \(13167998447866683762601/5158996582031250000\) | \(80609321594238281250000\) | \([2]\) | \(2949120\) | \(3.0940\) |
Rank
sage: E.rank()
The elliptic curves in class 24150bn have rank \(0\).
Complex multiplication
The elliptic curves in class 24150bn do not have complex multiplication.Modular form 24150.2.a.bn
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
