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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 33600l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.j6 | 33600l1 | \([0, -1, 0, 15967, -1092063]\) | \(109902239/188160\) | \(-770703360000000\) | \([2]\) | \(147456\) | \(1.5415\) | \(\Gamma_0(N)\)-optimal |
| 33600.j5 | 33600l2 | \([0, -1, 0, -112033, -11204063]\) | \(37966934881/8643600\) | \(35404185600000000\) | \([2, 2]\) | \(294912\) | \(1.8881\) | |
| 33600.j4 | 33600l3 | \([0, -1, 0, -592033, 165915937]\) | \(5602762882081/345888060\) | \(1416757493760000000\) | \([2]\) | \(589824\) | \(2.2346\) | |
| 33600.j2 | 33600l4 | \([0, -1, 0, -1680033, -837540063]\) | \(128031684631201/9922500\) | \(40642560000000000\) | \([2, 2]\) | \(589824\) | \(2.2346\) | |
| 33600.j3 | 33600l5 | \([0, -1, 0, -1568033, -954132063]\) | \(-104094944089921/35880468750\) | \(-146966400000000000000\) | \([2]\) | \(1179648\) | \(2.5812\) | |
| 33600.j1 | 33600l6 | \([0, -1, 0, -26880033, -53631540063]\) | \(524388516989299201/3150\) | \(12902400000000\) | \([2]\) | \(1179648\) | \(2.5812\) |
Rank
sage: E.rank()
The elliptic curves in class 33600l have rank \(1\).
Complex multiplication
The elliptic curves in class 33600l do not have complex multiplication.Modular form 33600.2.a.l
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
